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**Shurelia** Sorry to bother, this is may be simple problem, but this is sudden homework and must be presented in front of class, i'm affraid make a mistake.

1. prove that if p is prime number, and $\displaystyle {a}^{2}\equiv{b}^{2} mod p$, then $\displaystyle p|(a+b)$ and $\displaystyle p|(a-b)$

2. prove that $\displaystyle {n}^{13}-n$ is divisible by 2,3,5,7,13 fot any integer n

3. show that the product of three consecutive integers is divisible by 504 if the middle one is cube.

i take this from ivan niven , "introduction to number theory, fifth edition" page 57.

many thanks, i really need help.