## Romanian TST II 2011 Problem 4

Show that

(a) There are infinitely many positive integers such that there exists a square equal to the sum of the squares of consecutive positive integers (for instance, and are such, since , and ).

(b) If is a positive integer which is not a perfect square, and if is an integer number such that is a perfect square, then there are infinitely many positive integers such that is a perfect square.

Romanian TST 2011

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Categories: IMO, Number theory, Olympiad
IMO, TST

So these are all the tst problems? Wow they look very nice. Do you have solutions for these?

I haven’t thought very much on how to solve them, since I had a busy period with exams, but I’ll post solutions as soon as I have time. And I think there are more problems, but these are the ones I have until now.