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.

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Aug 11, 2018