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# Solve the following equation where each differently numbered a is considered a different variable:

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Solve the following equation where each differently numbered a is considered a different variable:

\begin{align*} a_1 + a_2 + a_3 &= 1, \\ a_2 + a_3 + a_4 &= 2, \\ a_3 + a_4 + a_5 &= 3, \\ a_4 + a_5 + a_6 &= 4, \\ a_5 + a_6 + a_7 &= 5, \\ a_6 + a_7 + a_8 &= 6, \\ a_7 + a_8 + a_9 &= 7, \\ a_8 + a_9 + a_{10} &= 8, \\ a_9 + a_{10} + a_{11} &= 9, \\ a_{10} + a_{11} + a_{12} &= 10, \\ a_{11} + a_{12} + a_{13} &= 11, \\ a_{12} + a_{13} + a_{14} &= 12, \\ a_{13} + a_{14} + a_{15} &= 13, \\ a_{14} + a_{15} + a_{16} &= 14, \\ a_{15} + a_{16} + a_{17} &= 15, \\ a_{16} + a_{17} + a_{1} &= 16, \\ a_{17} + a_{1} + a_{2} &= 17, \end{align*}

Aug 21, 2022

$$\displaystyle a_{1},a_{2},\dots,a_{16},a_{17}=0,6,-5,1,7,-4,2,8,-3,3,9,-2,4,10,-1,5,11$$