Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ON CONGRUENCES WITH THE TERMS OF THE SECOND ORDER SEQUENCES {Ukn} AND {Vkn}

  • KOPARAL, SIBEL (Department of Mathematics, Kocaeli University) ;
  • OMUR, Nese (Department of Mathematics, Kocaeli University)
  • Received : 2018.04.28
  • Accepted : 2018.06.29
  • Published : 2018.09.25
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Abstract

In this paper, we consider the congruences involving harmonic numbers and the terms of the sequences {$U_{kn}$} and {$V_{kn}$}. For example, for an odd prime number p, $${\sum\limits_{i=1}^{p-1}}H_i{\frac{U_{k(i+m)}}{V^i_k}}{\equiv}{\frac{(-1)^kU_{k(m+1)}}{_pV^{p-1}_k}}(V^p_k-V_{kp})(mod\;p)$$, where $m{\in}{\mathbb{Z}}$ and $k{\in}{\mathbb{Z}}$ with $p{\nmid}V_k$.

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References

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