# Negative powers of 4

Algebra Level pending

Let $$A = 1^{-4}+2^{-4}+3^{-4 }+4^{-4 }+5^{-4}+\cdots$$ denote the sum of the reciprocals of the fourth powers of all positive integers, and $$B = 1^{-4 }+ 3^{-4 }+ 5^{-4 }+ 7^{-4 }+ \cdots$$ a similar sum for all odd positive integers.

Let $$\dfrac AB = \dfrac CD$$, where $$C$$ and $$D$$ are coprime positive integers, find $$C+D$$.

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