PRIME SOLUTIONS TO POLYNOMIAL EQUATIONS IN MANY VARIABLES AND DIFFERING DEGREES
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DOI: 10.1017/fms.2018.21
Abstract: Let $\mathbf{f}=(f_{1},\ldots ,f_{R})$ be a system of polynomials with integer coefficients in which the degrees need not all be the same. We provide sufficient conditions for which the system of equations $f_{j}(x_{1},\ldots ,x_{n})=0~(1\leqslant j\leqslant R)$… read more here.
Keywords: polynomial equations; many variables; prime solutions; variables differing ... See more keywords
On the finiteness of solutions for polynomial-factorial Diophantine equations
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DOI: 10.1515/forum-2020-0138
Abstract: Abstract We study the Diophantine equations obtained by equating a polynomial and the factorial function, and prove the finiteness of integer solutions under certain conditions. For example, we show that there exist only finitely many… read more here.
Keywords: factorial diophantine; finiteness solutions; polynomial factorial; solutions polynomial ... See more keywords