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twin primes and diophatines

Source: Nigerian mthematics olympiad round 3 problem 4

February 21, 2020
number theoryDiophantine equation

Problem Statement

let ppand q=p+2q=p+2 be twin primes. consider the diophantine equation (+)(+) given by n!+pq2=(mp)2n!+pq^2=(mp)^2 m≥1m\geq1, n≥1n\geq1 i. if m=pm=p,find the value of pp. ii. how many solution quadruple (p,q,m,n)(p,q,m,n) does (+)(+) have ?
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