Linnik considered about 70 years ago the following approximation to the binary Goldbach problem. Is it possible to give a fixed integer K such that every sufficiently large even integer could be written as the sum of two primes and K powers of two? He solved the problem affirmatively with an unspecified large K. The first explicit result $$(K=54\,000)$$ appeared at the end of the 1990's. In the present work we show that $$K=8$$ powers of two suffices without supposing any unproved hypothesis.

中文翻译：

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林尼克对哥德巴赫问题的逼近。二

林尼克在大约 70 年前考虑了二元哥德巴赫问题的以下近似。是否有可能给出一个固定的整数 K，使得每个足够大的偶数都可以写成两个素数和 K 的两个幂的和？他用一个未指定的大 K 肯定地解决了这个问题。第一个显式结果 $$(K=54\,000)$$ 出现在 1990 年代末。在目前的工作中，我们表明 $$K=8$$ 两个的幂就足够了，而无需假设任何未经证实的假设。