Is this true: 'The only way you can get from one perfect square, q^2, to another, p^2, by multiplying by a constant [i.e. p^2=a^2 q^2] is if q IS that factor [i.e. q^2=a^2]'?

Question

Is this true: 'The only way you can get from one perfect square, q^2, to another, p^2, by multiplying by a constant [i.e. p^2=a^2 q^2]  is if q IS that factor [i.e. q^2=a^2]'?

hartnn · Answer

'the first square IS that factor'  what is 'that' here? factor of whose ?
$b^2=ma^2$

anonymous · Answer

$$q^2=49p^2$$Must $$q=49$$?

anonymous · Answer

I've edited it. Is that still ambiguous?

hartnn · Answer

then i don't think its always true....
q  equal 49, is not necessary

anonymous · Answer

Of course apart from the trivial case where p=1

anonymous · Answer

Counterexample: 6^2= 4 * 2^2

Damn, it's wrong!

hartnn · Answer

yea, its false....

anonymous · Answer

This popped up in http://www.komal.hu/verseny/feladat.cgi?a=honap&h=201210&t=mat&l=en if anyone's interested...