diophantine equation

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Joined: Aug 4, 2011

by hemangsarkar, Sep 24, 2015, 4:59 PM

Q) Suppose $a_1, a_2, a_3, a_4, a_5, a_6, a_7$ are integers such that

$\frac{5}{7}=\frac{a_2}{2!}+\frac{a_3}{3!}+\frac{a_4}{4!}+\frac{a_5}{5!}+\frac{a_6}{6!}+\frac{a_7}{7!}$

where $0 \le a_j < j$ for $j=2,3,4,5,6,7$ .

Find the value of $a_2 + a_3 + a_4 + a_5 + a_6 + a_7$

solution