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Find all (a,b) with a divides b+1 and b divides a^3-1

Source: XVIII Olimpíada Matemática Rioplatense (2009)

July 23, 2011

number theory unsolvednumber theory

Problem Statement

Find all pairs

(a,b)

of integers with

a>1

and

b>1

such that

a

divides

b+1

and

b

divides

a^3-1