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July 26

Conjecture about the product of two squares of certain form always being a perfect square?

I have a simple conjecture about the product of two squares of a certain form, namely: For any given N, ((N-2)^2)*((N+2)^2) is always a perfect square. Is this obvious or otherwise easy to prove? 70.112.97.77 (talk) 16:52, 26 July 2013 (UTC)[reply]

Consider a²b²=(ab)². RDBury (talk) 17:03, 26 July 2013 (UTC)[reply]

[SLAPS FOREHEAD] Right, thanks! 70.112.97.77 (talk) 17:10, 26 July 2013 (UTC)[reply]

To put it differently, the product of two squares is always a perfect square, they don't need to be of a certain form. -- Meni Rosenfeld (talk) 18:38, 27 July 2013 (UTC)[reply]

Measuring "Northness"

I posted this question about defining orientations on a sphere at the science desk, but it occurs to me that mathematics people might have a better time with it, so I thought to mention it here. Please post answers at the science desk. Dragons flight (talk) 22:47, 26 July 2013 (UTC)[reply]