(Note that pi should be taken as meaning p sub i. I don't know how to do formatting with this, and when I try, it removes it.) Prove that, for odd pi, we have ∑((pi-1)/2) is congruent to ((∏pi)-1)/2 mod 2.
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Hint : split up the $\displaystyle p_i$'s into two classes, according to whether they are $\displaystyle \equiv 1 \mod 4$ or $\displaystyle \equiv -1 \mod 4$.
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