Suppsoe a, b[tex]\in[/tex]natural numbers, and d=GCD(a,b). Then d^2=GCD(a^2,b^2). I need to find where the proof goes wrong.
The Attempt at a Solution
By hypothesis, we have that d divides a and d divides b, so there are integres s and t with a=ds and b=dt. Then a^2=d^2s^2 and so d^2 divides a^2. Similarily d^2 divides b^2. Thus d^2 is a common divisor of a^2 and b^2, as desired.