This is an exercise from a textbook in Portuguese.
Let $a,d$ be natural numbers and consider the sequence $a+0d$, $a+d, a+2d, a+3d,\dots$. Show that there is no square or there exist infinitely many squares.
I am not allowed to use $\gcd$, congruences or the Fundamental theorem of arithmetic, just Euclidean Division.
If there exists one square, then it is either of the form $3k$ or $3k+1$. But it doesn't help me.
I would appreciate your help!