Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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REPRESENTATION OF A POSITIVE INTEGER BY A SUM OF LARGE FOUR SQUARES

  • Received : 2015.12.01
  • Accepted : 2016.03.08
  • Published : 2016.03.30
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Abstract

In this paper, we determine all positive integers which cannot be represented by a sum of four squares at least 9, and prove that for each N, there are nitely many positive integers which cannot be represented by a sum of four squares at least $N^2$ except $2{\cdot}4^m$, $6{\cdot}4^m$ and $14{\cdot}4^m$ for $m{\geq}0$. As a consequence, we prove that for each $k{\geq} 5$ there are nitely many positive integers which cannot be represented by a sum of k squares at least $N^2$.

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Acknowledgement

Supported by : Gangneung-Wonju National University

References

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