# Find All The Equations !

Number Theory Level pending

Given $$216$$ equations that we can form from $$x^{12}+ ax^8+ bx^4+ c=y^6$$ where $$a , b , c$$ positive integers which satisfy $$3 \leq a \leq 5 , 4 \leq b \leq 12$$ , and $$1 \leq c \leq 8$$ . Let $$n$$ donate the number of those equations which are solvable in positive integers . Then, what is the value of $$n^{10^{2014}}$$ mod $$2014$$ ?

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