2012/001) Arithmetic sequence only 1 perfect square?

Can an infinite arithmetic sequence of positive integers contain exactly one perfect square? If so, which one?

Ans : NO

reason :
if it has one square without loss of generality we can assume that it is the 1st term ( deleting all terms to the left and let it be x^2 and common difference is d


then x^2 + 2dx + d^2 = x^2 + d ( 2x + d)

so the term (2x +d+1)th term is is perfect square

we can generalize if as

x^2 + 2ndx + (nd)^2 = x^2 + d(2nx + n^2d) and putting n = 1 on wards it shall have infinite perfect squares

so if it has at least one perfect square then it shall have infinite perfect squares