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Find All Primes Satisfying Given Equations

Source: Irish Mathematical Olympiad - Paper 1 - 2008 -Question 1

May 10, 2008
number theoryprime numbersnumber theory proposed

Problem Statement

Let p1,p2,p3 p_1, p_2, p_3 and p4 p_4 be four different prime numbers satisying the equations 2p_1 \plus{} 3p_2 \plus{} 5p_3 \plus{} 7p_4 \equal{} 162 11p_1 \plus{} 7p_2 \plus{} 5p_3 \plus{} 4p_4 \equal{} 162 Find all possible values of the product p1p2p3p4 p_1p_2p_3p_4
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