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Simple sum

Author: mathforces
Problem has been solved: 26 times

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Let $S=\sum\limits_{a=1}^{\infty} \sum\limits_{b=1}^{\infty} 2^{a+b} \cdot \frac{b+a \cdot sin^2(b)-b \cdot sin^2(a)}{3^{a+b}(a+b)} $. Find the largest prime divisor of $S \cdot 2^8 \cdot 3^3 -1$.





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