Thank you for responding to my previous question. Here is another question that puzzles me:
Prove that it is not possible to have the sum of the squares of 13 consecutive positive integers be a square.
Your help is very much appreciated. Thank you.Hi again Wallace,
Suppose that the smallest of the 13 integers is x then the sum of their squares is
which, when expanded, can be written
I expect that you know expressions for the two sequences above. Substituting these expressions shows why the sum of the squares of 13 consecutive positive integers can't be a square.Cheers,