6

Part of 2021 German National Olympiad

Problems(1)

u,v,w in arithmetic progression such that uv+1, vw+1, wu+1 perfect squares

Source: Germany 2021, Problem 6

Determine whether there are infinitely many triples

(u,v,w)

of positive integers such that

u,v,w

form an arithmetic progression and the numbers

uv+1, vw+1

wu+1

are all perfect squares.

number theorynumber theory proposedArithmetic ProgressionPerfect SquaresPerfect Square