







Divisibility of 3n^5+7n 
20161214 

Parag pose la question :
Question from Parag, a student:
if n is a natural number,then 3n^5+7n is divisible by
a)2
b)3
c)5
d)7
i got the answer but still i need a valid alternate approach. Penny Nom lui répond. 





4821x14y is an 8digit number divisible by 72 
20140806 

RAYA pose la question : if 4821x14y is an 8digit number divisible by 72. How many values can x and y take? Penny Nom lui répond. 





The square of any odd number, decreased by 1, is divisible by 8 
20121116 

bailey pose la question : Prove that the square of any odd number, decreased by 1, is divisible by 8 Penny Nom lui répond. 





The difference of the two numbers 
20100215 

Steve pose la question : The difference of the two numbers 'abcdef ' and ' fdebca ' is divisible by 271. prove
that b = d and c = e. Claude Tardif lui répond. 





How many combinations of 8614 are divisible by 7? 
20080122 

Rebecca pose la question : How many combinations of 8614 are divisible by 7 equally (with no remainder)? 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. 





Divisibility 
20070518 

Ashish pose la question : A number is divisible by 2^n if the last n digits of the number are divisible by 2^n.
Why? Penny Nom and Claude Tardif lui répond. 





Divisibility by each of the first ten counting numbers 
20051017 

Simon pose la question : determine smallest positive integer that is divisible by each of the first ten counting numbers Penny Nom lui répond. 





A 3 digit number divisible by 7 
20040503 

A student pose la question : We need to arrange 1,3 and 6 to form a 3 digit number that is divisible by 7. Penny Nom lui répond. 





Divisibility by 2 or 5 or both 
20031030 

Abdu pose la question : How many positive integers less than 1,001 are divisible by either 2 or 5 or both? Penny Nom lui répond. 





Three consecutive positive intergers 
20030209 

Yew pose la question : Prove that when we multiply any consecutive positive intergers, the result is always divisible by 6.
ex. (7)(8)(9) = 504 = 6 (84) Penny Nom lui répond. 





Divisibility of 5^{ 2002} 
20020825 

Simon pose la question : I need to ask you a question if 5^{ 2002} and 3^{ 2002} are divisible by 26. Penny Nom lui répond. 





Divisibility by 9 
20001024 

Kelera pose la question : If the sum of the digits of a number is divisible by 9, then the number itself it divisible by 9. Why is that? How do you explain this? Penny Nom lui répond. 





111...1222...2 
19990811 

Brad Goorman pose la question : Let N = 111...1222...2, where there are 1999 digits of 1 followed by 1999 digits of 2. Express N as the product of four integers, each of them greater than 1. Penny Nom lui répond. 





Divisibility of 2n choose n. 
19960924 

Kathy Doan pose la question : Can you prove that "2n choose n" is not divisible by 3, 5, and 7 for infinitely many n? Penny Nom lui répond. 

