One question about the sequence $a+0d$, $a+d, a+2d, a+3d,\dots$ where $a,d$ are natural numbers 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!

Hint: If $n^2 = a+dk$, show that $(n+d)^2 = a+dj$ for some $j$.
