# 6 Letters, 1 Number.

Level pending

How many ordered sets of integers $(a,b,c,d,e,f)$ are there such that it satisfies the equations below? $a^{5}=b\times c\times d\times e$ $b^{5}= c\times d\times e\times f$ $c^{5}=a\times d\times e\times f$ $d^{5}=a\times b\times e\times f$ $e^{5}=a\times b\times c\times f$ $f^{5}=a\times b\times c\times d$

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