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Seven eleven

Author: mathforces
Problem has been solved: 64 times

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There are seven real numbers $a_1, a_2, a_3, a_4, a_5, a_6, a_7$ such that $$a_1+a_2+a_3+a_4+a_5=3$$ $$a_2+a_3+a_4+a_5+a_6=4$$ $$a_3+a_4+a_5+a_6+a_7=5$$ $$a_4+a_5+a_6+a_7+a_1=6$$ $$a_5+a_6+a_7+a_1+a_2=7$$ $$a_6+a_7+a_1+a_2+a_3=8$$ $$a_7+a_1+a_2+a_3+a_4=9$$ The number $a_5$ can be represented as $\frac{m}{n}$ where $m$ is an integer, $n$ is a positive integer, and $m$ and $n$ are relatively prime. Find $m^2+n^2$.

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