Congruences

**Zennie** · March 10th 2010, 02:11 PM

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 $e \geq 0$ .

**aman_cc** · March 11th 2010, 07:55 AM

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?

**proscientia** · March 11th 2010, 12:52 PM

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 $e.$

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