+0

# Help with a few

+1
45
1
+48

For how many positive integers a<100 will a^3 +23 be divisible by 24?

What is the size of the largest subset ,s , of {1,2,3...50} such that no pair of distinct elements of  has a sum divisible by 7

Find the number of integral values of x for which the expression $$\frac {4^n + 15n - 1}{x}$$ has an integer value for every positive integer n.

Determine the smallest positive integer k such that $$60^n + k \cdot 71^n$$ is divisible by 1441 for all odd positive integers n.

Show that if x,y,z are integers such that $$x^3 + 5y^3 = 25z^3$$, then x = y = z = 0.

lololololololololll  Aug 11, 2018
#1
0

For how many positive integers a<100 will a^3 +23 be divisible by 24?

The following integers satisfy the condition:

1, 25, 49, 73, 97.

Note: They are obtained by using: 24n + 1, where n=0, 1, 2, 3, 4.

Guest Aug 12, 2018
edited by Guest  Aug 12, 2018