# Thread: some of congruence problems

1. ## some of congruence problems

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.

2. ## Re: some of congruence problems

Originally Posted by 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.

It seems to me that is homework assignment for a grade, and by forum's regulation we can't help you.

3. ## Re: some of congruence problems

Thread closed. You can PM me if you wish to discuss this further.

-Dan