Prove that a number of the form "abcabc" (i.e., a six-digit number formed by rep

Prove that a number of the form "abcabc" (i.e., a six-digit number formed by repeating a three-digit sequence) cannot be a perfect square.

Find all natural numbers p such that both p and 5p + 1 are prime numbers.

Interesting Problems

What is the remainder when dividing 9^2015 + 7^2015 - 2^2015 by 8?

The number A has 5 divisors, and the number B has 7 divisors. Can the product AB have exactly 10 divisors?

Prove that (abc - cba) is divisible by