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A quadratic polynomial $\Phi_{a,b,c}(x,y,z)=x(ax+1)+y(by+1)+z(cz+1)$ is called universal if the diophantine equation $\Phi_{a,b,c}(x,y,z)=n$ has an integer solution$x,y,z$ for any nonnegative integer $n$. In this article, we show that if $(a,b,c)=(2,2,6)$, $(2,3,5)$ or $(2,3,7)$, then $\Phi_{a,b,c}( x,y,z)$ is universal. These were conjectured by Sun in \cite {Sun}.
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참고문헌 (8)
참고문헌 신청
J. Ju / Ternary universal sums of generalized polygonal numbers
Y. Kitaoka / 1993 / Arithmetic of Quadratic Forms, Cambridge Tracts in Mathematics, 106 / Cambridge University Press
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B.-K. Oh / 2011 / Regular positive ternary quadratic forms / Acta Arith. 147(3):233~243
오병권 / 2011 / TERNARY UNIVERSAL SUMS OF GENERALIZED PENTAGONAL NUMBERS / 대한수학회지 48(4):837~847
Y. Kitaoka / 1993 / Arithmetic of Quadratic Forms, Cambridge Tracts in Mathematics, 106 / Cambridge University Press
0000
B.-K. Oh / 2011 / Regular positive ternary quadratic forms / Acta Arith. 147(3):233~243
오병권 / 2011 / TERNARY UNIVERSAL SUMS OF GENERALIZED PENTAGONAL NUMBERS / 대한수학회지 48(4):837~847
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