On the Partition of an Odd Number into Three Primes in a Prescribed Proportion

详细

We prove that, for any partition 1 = a + b + c of unity into three positive summands, each odd number n can be subdivided into three primes n = p_a(n) + p_b(n) + p_c(n) so that the fraction of the first summand will approach a, that of the second, b, and that of the third, c as n → ∞.