- #1

- 23

- 0

## Homework Statement

let n be an integer . Prove the congruence below.

n^21 [itex]\equiv[/itex] n mod 30

## Homework Equations

n^7 [itex]\equiv[/itex] n mod 42

n^13 [itex]\equiv[/itex] n mod 2730

## The Attempt at a Solution

to prove 30| n^21-n，it suffices to show 2|n^21-n,3|n^21-n,5|n^21-n

and how to prove them?