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p+q in terms of n when pq-1= n^3 for odd primes p,q (HOMC 2019 JI-7)

Source:

November 7, 2020

number theorydiophantineDiophantine equation

Problem Statement

Let

p

and

q

be odd prime numbers. Assume that there exists a positive integer

n

such that

pq-1= n^3

. Express

p+q

in terms of

n