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http://dx.doi.org/10.4134/BKMS.2014.51.5.1325

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)
Publication Information
Bulletin of the Korean Mathematical Society / v.51, no.5, 2014 , pp. 1325-1337 More about this Journal
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.
Keywords
last digit; last non-zero digit; $n^n$;
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