I just took a number theory midterm, the professor had a question the that said(adsbygoogle = window.adsbygoogle || []).push({});

"Show by induction that for all integers n, 4[tex]^{n}[/tex] is congruent to 1 +3n mod(9).

Now am I crazy or did the professor probably mean to say integers greater or equal to 0, or for any natural number n, ...

couldn't you show a counter example for instance n = -2, such that the congruence is false?

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# Congruence of all integers n, 4^n and 1 +3n mod(9)?

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