Let $ [\alpha] $ denote the integral part of the real number $ \alpha $, and let $ N $ be a sufficiently large integer. In this paper, we proved that for $ 1 < c < \frac{38}{29} $, almost all $ n\in(N, 2N] $ can be represented as $ [p_1^c]+[p_2^c]+[p_3^c]+[p_4^c] = n $, where $ p_1, p_2, p_3, p_4 $ are prime numbers.
Citation: Jing Huang, Wenguang Zhai, Deyu Zhang. On a Diophantine equation with four prime variables[J]. AIMS Mathematics, 2025, 10(6): 14488-14501. doi: 10.3934/math.2025652
Let $ [\alpha] $ denote the integral part of the real number $ \alpha $, and let $ N $ be a sufficiently large integer. In this paper, we proved that for $ 1 < c < \frac{38}{29} $, almost all $ n\in(N, 2N] $ can be represented as $ [p_1^c]+[p_2^c]+[p_3^c]+[p_4^c] = n $, where $ p_1, p_2, p_3, p_4 $ are prime numbers.
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Jing Huang, Wenguang Zhai, Deyu Zhang. On a Diophantine equation with four prime variables[J]. AIMS Mathematics, 2025, 10(6): 14488-14501. doi: 10.3934/math.2025652
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