Consider the following positive integers: $$a,a+d,a+2d,\dots$$ Suppose there is a perfect square in the above list of numbers. Then prove that there are infinitely many perfect square in the above list. How can I do this?
At first I started in this way: Let the $n$th term is perfect square. Therefore, $$t_n=a+(n-1)d=m^2.$$ Then I think that I will put values at the position of $n$. But I failed to find anything from this level. Can somebody help me?