Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A GENERALIZATION OF GAUSS' TRIANGULAR THEOREM

  • Ju, Jangwon (Department of Mathematical Sciences Seoul National University) ;
  • Oh, Byeong-Kweon (Department of Mathematical Sciences and Research Institute of Mathematics Seoul National University)
  • Received : 2017.07.18
  • Accepted : 2018.03.08
  • Published : 2018.07.31
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Abstract

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 [8].

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Acknowledgement

Supported by : National Research Foundation of Korea

References

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