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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