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

by mgiddy911
Tags: congruence, integers, mod9
 P: 332 I just took a number theory midterm, the professor had a question the that said "Show by induction that for all integers n, 4$$^{n}$$ 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?
 Quote by mgiddy911 I just took a number theory midterm, the professor had a question the that said "Show by induction that for all integers n, 4$$^{n}$$ 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?
 P: 1,059 The only residues are 1,4,7, so even if we use the inverses, it doesn't matter since $$\frac{1}{4}\equiv 7 mod 9$$