Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ARITHMETIC SUMS SUBJECT TO LINEAR AND CONGRUENT CONDITIONS AND SOME APPLICATIONS

  • Kim, Aeran (Department of Mathematics and Institute of Pure and Applied Mathematics, Chonbuk National University) ;
  • Kim, Daeyeoul (National Institute for Mathematical Sciences) ;
  • Sankaranarayanan, Ayyadurai (School of Mathematics, Tata Institute of Fundamental Research)
  • Received : 2014.02.15
  • Accepted : 2014.03.31
  • Published : 2014.06.25
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Abstract

We investigate the explicit evaluation for the sum $\sum_{(a,b,x,y){\in}\mathbb{N}^4,\\{ax+by=n},\\{C(x,y)}$ ab in terms of various divisor functions (where C(x, y) is the set of residue conditions on x and y) for various fixed C(x, y). We also obtain some identities and congruences as interesting applications.

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References

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