# Cyclically 91

Number Theory Level 5

Find the sum of integers $$c$$ for all triples of integers $$(a,b,c),$$ $$a\leq b \leq c,$$ that satisfy the system of equations $\begin{cases} a^2-bc=91\\ b^2-ac=91\\ c^2-ab=91 \end{cases}$

Details and assumptions

If a number $$c$$ appears in several different triples $$(a,b,c),$$ it must be counted with multiplicity.

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