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- W2353239067 abstract "In this paper,it is proved that the number of positive integral solutions to the diophantine equations x_1+2x_2+…+mx_m=n is Q(n,m),which is the unordered partition number of the positive integer n into m distinct parts.The explicit formulations for Q(n,4) and Q(n,5) are given from the relationship between Q(n,m) and P(n,m)(the unordered partition number of positive integer n into m part) as well as the explicit formulation of P(n,4) and A(n,5)(the number of nonnegative integral solutions to the diophantine equation x_1+2x_2+…+5x_5=n).Therefore the explicit formulations for the number of positive integral solutions for the diophantine equations x_1+2x_2+3x_3+4x_4=n and x_1+2x_2+3x_3+4x_4+5x_5=n are obtained." @default.
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- W2353239067 date "2006-01-01" @default.
- W2353239067 modified "2023-09-25" @default.
- W2353239067 title "On the Number of Positive Integral Solutions to a Kind of Diophantine Equations" @default.
- W2353239067 hasPublicationYear "2006" @default.
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