What Numbers Are Consecutive Perfect Squares?

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Square Root Day occurs on the following dates each century: The number of years between consecutive Square Root Days in a century are consecutive odd numbers: 3, 5, 7, 9, 11, 13, 15, 17. This illustrates the fact that every odd number is the difference of two consecutive squares . ^ Wong, Nicole C. (2004-02-02). “A day getting to the root”.

How to prove that any consecutive perfect squares have odd difference?

You want to prove that any consecutive perfect squares have odd difference; let n 2 be the first one, so that ( n + 1) 2 is the larger one (make sure you can convince yourself that these really do represent consecutive squares). Now compute and see what you conclude about it.