E405 -- Solutio problematis, quo duo quaeruntur numeri, quorum productum tam summa quam differentia eorum sive auctum sive minutum fiat quadratum

(A solution of a problem about two numbers which are searched for, of which their product, increased or decreased by their sum or difference, will be a square)


Euler wants to find a and b such that the following four quantities are all squares: ab+a+b, ab+a-b, ab-a+b, and ab-a-b.

According to the records, it was presented to the St. Petersburg Academy on March 5, 1770.

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