MathDB

Prime Diophantine

Source: Pan-American Girls’ Mathematical Olympiad 2022, Problem 2

October 27, 2022

number theoryPAGMODiophantine equation

Problem Statement

Find all ordered triplets

(p,q,r)

of positive integers such that

p

and

q

are two (not necessarily distinct) primes,

r

is even, and

p^3+q^2=4r^2+45r+103.