E560 -- Miscellanea analytica
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.
Originally published in Opuscula Analytica 1, 1783, pp. 329-344
Opera Omnia: Series 1, Volume 4, pp. 91 - 104
- Reprinted in Commentat. arithm. 2, 1849, pp. 44-52 [E560a]
- Original Publication: E560
- Italian translation (Francesco Venti): E560
Return to the Euler Archive