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Diophantine - Find all (a,b,p)

Source: Italy TST 2003

November 9, 2010
modular arithmeticnumber theory proposednumber theory

Problem Statement

Find all triples of positive integers (a,b,p)(a,b,p) with a,ba,b positive integers and pp a prime number such that 2a+pb=19a2^a+p^b=19^a
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