ON THE LAST DIGIT AND THE LAST NON-ZERO DIGIT OF nnIN BASE b

Jose Maria Grau, Antonio M. Oller-Marcen
2014 Bulletin of the Korean Mathematical Society  
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
more » ... square-free. We also show that if b = 2 2 s the sequence is periodic and conjecture that this is the only such case.
doi:10.4134/bkms.2014.51.5.1325 fatcat:k32r6rawk5gargg5n4piryb2yq