Sunday, October 8, 2017

elementary number theory - Prove/disprove: if $a^2$ divides $ b^3$, then $a$ divides $b$

Prove/disprove the following: if $a^2$ divides $b^3$, then $a$ divides $b$



I've tried rewriting as $b^3=a^2c$, but I can't seem to show anything else for $c$. If I can prove that it is/isn't an integer, that would prove the whole thing for me.

No comments:

Post a Comment

analysis - Injection, making bijection

I have injection $f \colon A \rightarrow B$ and I want to get bijection. Can I just resting codomain to $f(A)$? I know that every function i...