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- W2921295231 abstract "This paper concerns the solvability of the prime variables equations $a_1p_1^2+a_2p_2^2+~a_3p_3^2+a_4p_4^3+a_5p_5^3$ $+,~a_6p_6^3=b$, where $a_1,a_2,ldots,a_6$ are non-zero integers and $b$ is any integer. Suppose that $a_1,a_2,ldots,a_6$ satisfy some related conditions. Using the circle method we prove that(i) if all $a_1,a_2,ldots,a_6$ are positive, and $bgg~max~{|a_j|}^{33+varepsilon}$, then the equation is soluble in primes $p_j$, $j=1,ldots,6$, and (ii) if $a_1,a_2,ldots,a_6$ are not all of the same sign, then the equation has prime solutions satisfying $max~{~p_1^2,p_2^2,p_3^2,p_4^3,p_5^3,p_6^3~}ll~|b|+max~{|a_j|}^{32+varepsilon}$." @default.
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- W2921295231 date "2019-03-07" @default.
- W2921295231 modified "2023-10-05" @default.
- W2921295231 title "Small prime solutions of equations with powers 2 and 3" @default.
- W2921295231 doi "https://doi.org/10.1360/n012018-00201" @default.
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