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n divides m^2+1 and m divides n^2+1

Source: South African MO 1995 Q6

May 27, 2012

algebrapolynomialVietafunctionnumber theory unsolvednumber theory

Problem Statement

Find all pairs

(m,n)

of natural numbers with

m<n

such that

m^2+1

is a multiple of

n

and

n^2+1

is a multiple of

m