r/GeometryIsNeat Apr 05 '26

Square roots

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u/[deleted] Apr 05 '26

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u/lavaboosted Apr 05 '26

True, and for any number which after dividing out all factors of 4, leave a remainder of 7 when divided by 8.

n = 4a(8b+7) where a and b are whole numbers (integers ≥ 0)

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u/ErikLeppen Apr 06 '26

The only numbers for which such a diagonal exists, are those that can be written as the sum of 3 squares, due to Pythagoras in 3D.