1. The problem statement, all variables and given/known data For some field F, if a and b are two elements which are not squares but whose product is a square, show that there is an element k such that [itex] a = k^2 b [/itex]. 3. The attempt at a solution This is a boiled down version of what I'm actually trying to show, so the statement above may not actually be correct. If it's not, please let me know! I have a few ideas of how to hit this, but the following is the one I like the most: If [itex] ab = c^2 [/itex] for some element [itex] c \in F [/itex] then it is sufficient to show that either [itex] a | c [/itex] or [itex] b | c[/itex], since then (without loss of generality) if [itex] a | c [/itex] then there is some constant k such that ak = c in which case [itex] ab = a^2 k^2 [/itex] which implies that [itex] b = k^2 a [/itex]. Now the hard part (for me at least!) is showing that [itex] ab = c^2 [/itex] implies that either a|c or b|c. It seems like this result should be true, but I've been having trouble showing it. I start like this. If both a|c and b|c then we are done, hence assume without loss of generality that [itex] b \not| c[/itex]. Here is where I get stuck. Any ideas?