# ON A WARING-GOLDBACH PROBLEM INVOLVING SQUARES, CUBES AND BIQUADRATES

• Liu, Yuhui (School of Mathematical Sciences Tongji University)
• Accepted : 2018.10.11
• Published : 2018.11.30

#### Abstract

Let $P_r$ 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, the equation $$N=x^2+p_1^2+p_2^3+p_3^3+p_4^4+p_5^4$$ is solvable with x being an almost-prime $P_4$ and the other variables primes. This result constitutes an improvement upon that of $L{\ddot{u}}$ [7].

#### Acknowledgement

Supported by : National Natural Science Foundation of China

#### References

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