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Systems of easyuations

Source: 2019 AIME II problem 3

March 22, 2019
AMCAIMEAIME IIalgebrasystem of equations2019 AMC2019 AIME II

Problem Statement

Find the number of 77-tuples of positive integers (a,b,c,d,e,f,g)(a,b,c,d,e,f,g) that satisfy the following systems of equations: \begin{align*} abc&=70,\\ cde&=71,\\ efg&=72. \end{align*}