# Math Help - proof

1. ## proof

Prove that 2 divides n^21-n.

2. Originally Posted by meshel88
Prove that 2 divides n^21-n.
We only have two cases, either $n\equiv 0\text{ mod }2\implies n^{21}\equiv 0^{21}=0\equiv n\text{ mod }2$ or $n\equiv 1\text{ mod }2\implies n^{21}\equiv 1^{21}=1\equiv n\text{ mod }2$

3. In other words...

a) for $n$ even also $n^{21}$ is even so that $n^{21}-n$ is even...

b) for $n$ odd also $n^{21}$ is odd so that $n^{21}-n$ is even...

Kind regards

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