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

Source: Germany 2021, Problem 6

June 16, 2021

number theorynumber theory proposedArithmetic ProgressionPerfect SquaresPerfect Square

Problem Statement

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

and

wu+1

are all perfect squares.