An algebraic problem of finding four numbers with the sum of the three others
Euler considers the following problem: Given a, b, c, d with a = v(x+y+z), b = x(v+y+z), c = y(v+x+z), and d = z(v+x+y), determine v, x, y, and z. He changes variables to arrive at four "nice" equations, each in terms of a new variable u and the constants a, b, c, and d.
Original Source Citation
Opera Postuma, Volume 1, pp. 282-287.
Opera Omnia Citation
Series 1, Volume 6, pp.494-503.