# Math question Pythagorean squares

**URL:** <https://boards.straightdope.com/t/math-question-pythagorean-squares/760184>\
**Category:** Factual Questions\
**Created:** [July 18, 2016, 3:19am UTC](https://boards.straightdope.com/t/math-question-pythagorean-squares/760184 "2016-07-18T03:19:57Z")\
**Posts on this page:** 2\
**Page:** 2

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**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\
**Post date:** [July 19, 2016, 9:40pm UTC](https://boards.straightdope.com/t/math-question-pythagorean-squares/760184/21 "2016-07-19T21:40:38Z")

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If you want to see a constructive proof (modulo factoring the number into primes) that every positive integer is a sum of four squares, look here: [Every positive integer is a sum of four integer squares](https://www.alpertron.com.ar/4SQUARES.HTM). Note that the formula that could have been derived using quaternionic norms is just stated as such. I assume the formula itself is older than quaternions, although I don’t know that.

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**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\
**Post date:** [July 20, 2016, 12:50am UTC](https://boards.straightdope.com/t/math-question-pythagorean-squares/760184/22 "2016-07-20T00:50:37Z")

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Still digesting your posts, but wanted to say thanks in the meantime. The X_conj(X) thing should have been obvious–my intuition was right, but I didn’t (quite) make the simple leap that since it always comes to a non-complex number, it must just be a scaled version of the other one (i.e., non-primitive). Or the degenerate case of a^2+0 in the case of X_conj(X)_Y_conj(Y).

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