| 吕晓东.华林-哥德巴赫问题: 两个平方, 两个立方和两个四次方[J].数学年刊A辑,2015,36(2):161~174 |
| 华林-哥德巴赫问题: 两个平方, 两个立方和两个四次方 |
| Waring-Goldbach Problem: Two Squares, TwoCubes and Two Biquadrates |
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| DOI： |
| 中文关键词: 华林-哥德巴赫问题, 圆法, 筛法, 殆素数 |
| 英文关键词:Waring-Goldbach problem, Circle method, Sieve method,
Almost-prime |
| 基金项目:国家自然科学基金 (No.10000000) 资助的项目. |
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| 中文摘要: |
| 令$P_r$表示素因子不超过 $r$ 的殆素数, 按重数计. 作者证明了对于充分大的偶数 $N$, 方程
$$N=x^2+p_1^2+p_2^3+p_3^3+p_4^4+p_5^4$$
有解, 其中 $x$ 是殆素数 $P_6$, $p_j\,(j=1, \cdots, 5)$ 是素数. |
| 英文摘要: |
| Let Pr denote an almost-prime with at most r prime factors, counted according
to multiplicity. In this paper it is proved that for every sufficiently large even integer N, theequation
N = x2 + p21
+ p32
+ p33
+ p44
+ p45
is solvable with x being an almost-prime P6 and the pj (j = 1, · · · , 5) are primes. |
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