Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON THE LAST DIGIT AND THE LAST NON-ZERO DIGIT OF nn IN BASE b

  • Grau, Jose Maria (Departamento de Matematicas Universidad de Oviedo) ;
  • Oller-Marcen, Antonio M. (Centro Universitario de la Defensa)
  • Received : 2012.04.13
  • Published : 2014.09.30
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Abstract

In this paper we study the sequences defined by the last and the last non-zero digits of $n^n$ in base b. For the sequence given by the last digits of $n^n$ in base b, we prove its periodicity using different techniques than those used by W. Sierpinski and R. Hampel. In the case of the sequence given by the last non-zero digits of $n^n$ in base b (which had been studied only for b = 10) we show the non-periodicity of the sequence when b is an odd prime power and when it is even and square-free. We also show that if $b=2^2{^s}$ the sequence is periodic and conjecture that this is the only such case.

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References

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