Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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THE NUMBERS THAT CAN BE REPRESENTED BY A SPECIAL CUBIC POLYNOMIAL

  • Published : 2010.04.30
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Abstract

We will show that if d is a cubefree integer and n is an integer, then with some suitable conditions, there are no primes p and a positive integer m such that d is a cubic residue (mod p), $3\;{\nmid}\;m$, p || n if and only if there are integers x, y, z such that $$x^3\;+\;dy^3\;+\;d^2z^3\;-\;3dxyz\;=\;n$$.

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References

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