A Chain of Products

★ 4/10combinatorics Diophantine Equations number theory Counting

Problem

Find the number of $7$ -tuples of positive integers $(a, b, c, d, e, f, g)$ that satisfy the system

\begin{cases} abc = 70, \\ cde = 71, \\ efg = 72. \end{cases}

Answer

Solution

Difficulty	4/10
Topics	combinatorics, Diophantine Equations, number theory, Counting

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