E560 -- Miscellanea analytica

(Miscellaneous analyses)


This starts with a proof of what Euler calls Waring's theorem, now known as Wilson's theorem, that (n-1)! is congruent to 1 modulo n if n is prime. The next problem is to find four numbers such that their pairwise products, increased by 1, give squares. He cites the problem posed by Leibniz: Find two numbers, p and q, whose sum is a square and the sum of their squares is a fourth power.

According to the records, it was presented to the St. Petersburg Academy on November 15, 1773.

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