0
$\begingroup$

let d,k be integers, with k even.

suppose d|2k

suppose d does not divide 2

suppose d does not divide k

show that d equals 2k.

(I'm really just trying to understand the 2nd last line, in this answer to the question: Prove that if $p$ is an odd prime that divides a number of the form $n^4 + 1$ then $p \equiv 1 \pmod{8}$)

1 Answers 1

3

It's not true. Take $k=6$ and $d = 4$ for example.

  • 0
    @confused I don't know what the purpose of that answer was. It looks like he wanted to generalize the question to other powers of $k$, but this generalization isn't correct (with $k = 6$, $5$ is an odd divisor of $2^6 + 1$ and is not $\equiv 1 \bmod 2*6$.)2012-08-18