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2 $begingroup$ Let $$A={frac{1}{2^2},frac{1}{3^2},frac{1}{5^2},...}$$ be the set of squares of the reciprocals of prime numbers. We have $$sum_{xin A}x < infty$$ Do there exist $B subset A$ , $C subset A$ , $B cap C = emptyset$ , such that $$sum_{xin B}x = sum_{xin C}x ?$$ It is important that we deal with primes and not with all natural numbers, otherwise we would have infinitely many solutions, as described in Wikipedia. number-theory prime-numbers share | cite | improve this question edited 12 hours ago co.sine