On the diophantine equation \(1+x+y=z\)
The authors use some elementary technics developed by them and J. L. Brenner, to solve the equation \(1+x+y=z\) in positive integers \(x,y,z\) divisible only by 2,3,5. The method involves the careful consideration of the equation modulo a series of primes, prime powers and other moduli. First, the simpler case is considered, when \(xyz\) is divisible by at most two of 2,3,5 only. In the general case elementary properties of the equation are established, together with bounds for certain exponents. The solutions with ``small'' exponents are found with computer assistence.
scientific article; zbMATH DE number 61916