# Congruences

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• Mar 10th 2010, 02:11 PM
Zennie
Congruences
Using the fact that $aa' \equiv bb' (mod m)$, prove that if $a \equiv b (mod m)$ then $a^e \equiv b^e (mod m)$ for any $e \geq 0$.
• Mar 11th 2010, 07:55 AM
aman_cc
Quote:

Originally Posted by Zennie
Using the fact that $aa' \equiv bb' (mod m)$, prove that if $a \equiv b (mod m)$ then $a^e \equiv b^e (mod m)$ for any $e \geq 0$.

are you sure u hv the complete question here?
• Mar 11th 2010, 12:52 PM
proscientia
Quote:

Originally Posted by Zennie
Using the fact that if $\color{red}a\equiv b\!\pmod m$ and $\color{red}a'\equiv b'\!\pmod m$ then $\color{red}aa' \equiv bb'\!\pmod m\color{black},$ prove that if $a \equiv b (mod m)$ then $a^e \equiv b^e (mod m)$ for any $e \geq 0$.

Use induction on $e.$