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تسجيل مستخدم جديدTheoremata arithmetica nova methodo demonstrata
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Euler presents a third proof of the Fermat theorem, the one that lets us call it the Euler-Fermat theorem. This seems to be the proof that Euler likes best. He also proves that the smallest power x^n that, when divided by a numer N, prime to x, and that leaves a remainder of 1, is equal to the number of parts of N that are prime to n, that is to say, the number of distinct aliquot parts of N. The translation is presnted from Eulers Latin original into German.
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Translated from the Latin original Novae demonstrationes circa resolutionem numerorum in quadrata (1774). E445 in the Enestrom index. See Chapter III, section XI of Weils Number theory: an approach through history. Also, a very clear proof of the fou
r squares theorem based on Eulers is Theorem 370 in Hardy and Wright, An introduction to the theory of numbers, fifth ed. It uses Theorem 87 in Hardy and Wright, but otherwise does not assume anything else from their book. I translated most of the paper and checked those details a few months ago, but only finished last few parts now. If anything isnt clear please email me.
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