







A graph with 100 vertices and one edge 
20220111 

Maftuna pose la question : A graph has 100 vertices and only one edge. How many connected components does it
have? Penny Nom lui répond. 





A question about the empty set 
20180617 

Andrey pose la question : Hello there!
I got that an empty set is a subset of every set.
There is a question.
Is an empty set an element of every set?
∅ ⊆ {x}True
∅ ∈{x}?
Sorry if the question is easy. A set theory is a bit confusing. Penny Nom lui répond. 





n^2 is a multiple of 100 
20150330 

Rahul pose la question : I have to prove that n^2 is a multiple of 100 is necessary or
Sufficient condition (or both) for n being multiple of 10 Penny Nom lui répond. 





The product of a 2digit number and a 3digit number 
20150206 

Nathaniel pose la question : The product of a 2digit number and a 3digit number is about 50 000 what are the products Penny Nom lui répond. 





A union and interception problem 
20131019 

Zakir pose la question : Sir, I have some problem in union there is a Question in a book
find B set if A={2,4,6,8} , AUB={2,4,5,6,7,8} and A intersection B={6,8}
plz tell me how can I find the B set Penny Nom lui répond. 





Restricted partitions 
20130325 

vidya pose la question : I am having a series of numbers eg.( 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15)
I can take any 5 digits eg(15,10,8,6,5) and it should not repeat and the summation should be any predefined static value . eg(44)
That is (15+10+8+6+5=44) . How many summation series will result 44 ?
My problem is how to find this using a formula or any other simpler automation method is there instead of checking one by one all the combinations.
Plz do help me... Thnks in advance Chris Fisher lui répond. 





Prove A intersect B =X iff A = X and B = X 
20100306 

Gloria pose la question : how would you prove A intersect B =X iff A = X and B = X Tyler Wood lui répond. 





The sum of digits of 4444^4444 
20090831 

SHIVDEEP pose la question : The sum of digits of 4444^4444 is A .The sum of digits of A is B .
Find the sum of digits of B ? Claude Tardif lui répond. 





30 students 
20090806 

Peter pose la question : Question from Peter, a student:
Can you please help with the following questions?
(a) It is known that among any group of the three students in a class two of them are friends. Total number of students is 25. Prove that there is a student who has at least 12 friends.
(b) There are 30 students in a class. They sit at 15 double desks, each one is for two students. Half of the girls sit with boys. Is it possible to make a rearrangement so that half of the boys sit with girls? Penny Nom lui répond. 





Divisibility 
20090617 

Sophia pose la question : Hello
Please help my son with the solutions to the following:
a) Determine the remainder when 2^2009 + 1 is divided by 17;
b) Prove that 30^99 + 61^100 is divisible by 31;
c) It is known that numbers p and 8p^2+1 are primes. Find p.
Again, your assistance is greatly appreciated.
Thanks
Sophia Robert Dawson lui répond. 





GCD (a + b, a  b). 
20090401 

Tomas pose la question : Let a and b integer and relatively prime. Prove that:
GCD (a + b , a  b) = 1 or 2 Stephen La Rocque lui répond. 





More on infinity and Set Theory 
20090217 

Justin pose la question : I greatly appreciate your help I was just wondering from your previous answer, why doesn't Cantor's cardinal numbers in set theory apply to the limit x>0, y=infinity?
Justin Robert Dawson lui répond. 





Infinity and Set Theory 
20090217 

Justin pose la question : I was just wondering is the limit x>0, y=1/x=infinity, the biggest uncountable infinity according to Cantor's cardinal numbers in set theory?
Justin Robert Dawson lui répond. 





Some number theoretic speculations 
20081204 

Andrew pose la question : Another way of looking at the 'alternating parity polynomial', again based on Fermat's Little Theorem,
is to substitute (a  b) for x in x^(p1)  1 as this is always divisible by any prime p. So, if one removes
the " 1", there is always a remainder of (1/p)! (I took up your challenge!)
. . .
Andrew Chris Fisher and Victoria West lui répond. 





Finding the last nonzero digits of large factorials 
20071004 

Mukesh pose la question : i have to find last five non zero digits of integer which can be very large (
upto 10^12) . i can find last non zero digit of of any factorial. Now my problem is that
i have to find last five non zero digit of factorial and also i want to general method for
last K non zero digits of factorial n. For example 10!=3628800 so last non zero digit is 8 ,last two
non zero digit is 88 .....and last five non zero digit is 36288. Victoria West lui répond. 





A question about integers 
20070824 

Jerry pose la question : Does there exist a positive integer such that when it is written in base 10 and its leftmost digit is crossed out, the new number is 56 times less than the original number? Stephen La Rocque and Penny Nom lui répond. 





Induction  divisibility 
20070804 

Jerry pose la question : How would you prove that for any positive integer n, the value of the expression 3^(2n+2)  8n 9 is divisible by 64. Chris Fisher and Penny Nom lui répond. 





A problem involving squarefree integers 
20070507 

Andrew pose la question : I was told that if x > y (integers); then x would never exactly =
divide y^n (n integer > 1) if (x,y) =3D 1 ; or if x is "square =
free". Is the latter true and why? Stephen La Rocque and Penny Nom lui répond. 





The tens digit of a really large number 
20070305 

Sai pose la question : How can i find the tens digit of a really large number? i was gven 63^15 + 15^63 in a competitive exam. Penny Nom lui répond. 





An even positive integer cubed minus four times the number 
20070207 

Rachael pose la question : I can't figure out the proof or the method to get the proof for this question: any even positive integer cubed minus four times the number is divisible by 48 Haley Ess and Penny Nom lui répond. 





11^n +22^n = 55^n 
20070129 

Ankit pose la question : 11^n +22^n = 55^n
find the value of n? Penny Nom lui répond. 





1X2X3X4+1=5^5 
20061123 

Liza pose la question : 1X2X3X4+1=5 square 2x3x4x5+1=11 square What is the rule for this? Stephen La Rocque and Penny Nom lui répond. 





Pick any prime number greater than 3,square it ,then ... 
20061120 

Eliseo pose la question : I was ask to pick any prime number greater than 3,square it ,then subtract 4, then divide the new result by 12 and record the remainder. He told me the remainder was 9. How could he be sure that the remainder was 9 without knowing which prime I picked? Stephen La Rocque lui répond. 





A number theory problem 
20060505 

DeHayward pose la question : Find the 6digit number in which the first digit is one less than the second, the third is half of the second, the fourth is 3 times the third, and the last 2 digits are the sum of the fourth and fifth. The sum of all the digits is 24. Paul Betts lui répond. 





The sum of a three digit number and its three individual digits is 429 
20060408 

Megan pose la question : Gill has recently moved to a new house, which has a three digit number. the sum of this number and its three individual digits is 429. What is the product of the three digits which make up the house number? Chris Fisher lui répond. 





Tables with perfect squares 
20051130 

Craig pose la question : A table consists of eleven columns. Reading across the first row of the table we find the numbers 1991, 1992, 1993,..., 2000, 2001. In the other rows, each entry in the table is 13 greater than the entry above it, and the table continues indefinitely. If a vertical column is chosen at random, then the probability of that column containing a perfect square is: Claude Tardif lui répond. 





n^2+n1 has no divisors ending with 3 or 7 
20050908 

Arne pose la question : at least it seems like for any integers n and k,
10k+3 and 10k+7 do not divide n²+n1
I tested this for every n from 0 to 3200 (which means same for the numbers from 3201 to 1)
could this be true, or is it just coincidence, or am I just totally wrong? Richard McIntosh lui répond. 





The numbers p and 8p^2 +1 are prime. 
20050530 

Antonio pose la question : The numbers p and 8p^{2} +1 are prime. Prove that the number 8p^{2}+2p+1 is also a prime number. Claude Tardif and Penny Nom lui répond. 





Divisibility of a^2 + b^2 
20050516 

Ampa pose la question : given natural numbers a and b such that a^{2}+b^{2} is divisible by 21, prove that the same sum of squares is also divisible by 441. Penny Nom lui répond. 





Matrices 
20031205 

Julie pose la question : I am doing a project and need to find some mathematiciens who had an influence in matrices. I can't seem to find any when I search online. Could you please help me with this? Judi McDonald lui répond. 





39 consecutive natural numbers 
20030819 

A student pose la question : Prove that among any 39 consecutive natural numbers it is always possible to find one whose sum of digits is divisible by 11. Penny Nom lui répond. 





abc,abc 
20021120 

Pam pose la question : Prove or disprove that "every number of the form abc,abc (where a, b, and c represent digits) is divisible by 7,11, and 13" Penny Nom lui répond. 





Relatively prime 
20021004 

Natasha pose la question : I really need help with this middle level math question. My little brother is asking me and I have no clue what the answer is. Explain what it means when two numbers are negatively prime. (?) Kathy Nolan and Penny Nom lui répond. 





When is 1! + 2! + 3! + ... + x! a square? 
20020819 

Sarathy pose la question : Solve : 1! + 2! + 3! + ... + x! = y^{ 2} How do i find the solutions ? Claude tardif lui répond. 





n +1, n+2, n+3, and n+4 are all composite 
20020409 

Jonathan pose la question : Find the small integer n such that n +1, n+2, n+3, and n+4 are all composite Penny Nom lui répond. 





Is n^2  2 a multiple of n  4? 
20010110 

John pose la question : Find all positive integers n so that n^{2}  2 is a multiple of n  4. Sukanta Pati lui répond. 





Divisibility by 16 
20001212 

Shiling pose la question : A number can be divided by 16 if and only if its 1st four digits can be divided by 16. How can you prove that? Penny Nom lui répond. 





A chemist had 8 flasks 
20001210 

Jimmy pose la question : A chemist had 8 flasks capable of holding 12, 15, 27, 35, 37, 40, 53 and 69 fluid ounces respectively. He filled some with water and then filled all the rest except one with alcohol. He used exactly one and a half times as much alcohol as water. Which flask was left empty and which were left with water and which with alcohol? Claude Tardif lui répond. 





Perfect numbers 
20001031 

A student pose la question : I was wondering if you could help me answer a question my prealgebra teacher asked in class the other day. He asked if we knew what the perfect numbers where. He told us the first number is 6 the second number is 28 but the third he did not tell us. Do you know what the third perfect number is? Paul Betts and Chris Fisher lui répond. 





A zip code problem 
20001026 

Rob Mathis pose la question : Find the zip code of a place in a county so that the product of it and the zip code of another place in another county of the same name, but in a different state, is an exact multiple of the number 123456789 Claude Tardif lui répond. 





How many 17's and 19's total 1000? 
20000907 

Jonathan pose la question : My question is: what 2 numbers would multiply 17 and 19 for a total of 1000. The numbers should not contain any decimal. Penny Nom lui répond. 





n^{3} + 2n^{2} is a square 
20000904 

David Xiao pose la question : determine the smallest positive integers, n , which satisfies the equation n^{3} + 2n^{2} = b where b is the square of an odd integer Harley Weston lui répond. 





Three consecutive odd integers 
20000818 

Wallace pose la question : A sixdigit integer XYXYXY, where X and Y are digits is equal to five times the product of three consecutive odd integers. Determine these three odd integers. Paul Betts lui répond. 





Five times a cube equals three times a fifth power 
20000705 

Harman Chaudhry pose la question : Which is the smallest 10digit number to be five times the cube of one number and also three times the fifth power of another? Penny Nom lui répond. 





Problems 
20000606 

Debbie Cummins pose la question : I am a Mum of a 12 yr.boy needing help with some math problems. I need not only the answers but how it is worked out.  Both the leftmost digit & the rightmost digit of a 4 digit number N are equal to 1. When these digits are removed, the 2 digit number thus obtained is N div by 21 Find N.
 Find all 3 digit even numbers N such that 693xN is a perfect square, that is, 693x N = k x k where k is an integer.
. . . Paul Betts and Claude Tardif lui répond. 





How many zeros? 
20000409 

Greg Potts pose la question : The natural numbers 1 to 25 are multiplied together (1 x 2 x 3x..24 x 25). How many zeros are there in the product of this multiplication? a)6 b)7 c)5 d)10 or e)4? Harley Weston lui répond. 





Party favors 
20000222 

Krystina Fernandez pose la question : Luanne was making party favors for her little sister's birthday party. Each party favor was in the shape of a cube. Luanne had pink and purple paint to paint the cubes and she could paint each face only solid pink or solid purple (no dots,stripes,ect.).For example, one cube may be all purple, another may have two purple faces and four pink faces. Her little sister wanted to have a different cube for each guest.(A cube is not considered different if it can be turned so that all it's sides match the corresponding sides of another cube.)How many different cubes was it possible for Luanne to make? Claude Tardif lui répond. 





Crossing number 
19991106 

Christian pose la question : The crossing number of a graph G, denoted cr(G) is defined to be the minimum number of (pairwise) crossings of edges among all drawings of the graph in the plane. For example, cr(K5)=1 and cr(K3,3)=1. What is cr(K7,7)? I figured out that the answer is 81. Now I am trying to figure out if K7,7 can be drawn in the plane with less than 81 crossings? I'm not sure how to approach this one. Other than actually drawing it out and checking by trial and error, I am not sure how to approach this problem. Please help! Denis Hanson lui répond. 





The sum of the cubes is the square of the sum 
19990825 

Bernard Yuen pose la question : How to prove 1^{3} + 2^{3} + 3^{3} + 4^{3} + ... n^{3} is equal to (1+2+3+...n)^{2}? (for n is positive integer) Harley Weston lui répond. 





Pick any odd number, square it, and then divide it by 8 
19981127 

Brenda Meagher pose la question : Pick any odd number, square it, and then divide it by 8. No matter what odd number is chosen and squared and divided by 8, the remainder is one. Could you please explain this to me or is there a pattern that I am not aware Harley Weston lui répond. 





Five Factors 
19980919 

Derek Yau pose la question : To whom it may concern, I have difficulty in getting the solution to the following question: Find 5 numbers that have exactly 5 factors. I got 16, 81 but couldn't find the rest. I believe that in order to have 5 factors, it has to be a square number. Isn't it true? I guess there may be a pattern to this. Thanks for your help. Derek Yau. Penny Nom lui répond. 





When is ( n^3+1)/(mn1) an integer? 
19970211 

Ronald Lui pose la question : Determine all ordered pairs (m,n) of positive integers such that ( n^3+1)/(mn1)is an integer. Richard McIntosh lui répond. 

