Any number may be written in many different ways, using different strings in different bases. In few, very special cases, a symmetry emerges which is usually hidden beneath the surface: 230164 and 164230 are both equal to 54284 in base ten. This article analyzes the solution set to the (constrained) Diophantine equation that implements such symmetry, culminating in a conjecture on the number of solutions of the equation.
Arnone, S., Falcolini, C., Moauro, F., Siccardi, M. (2017). On Numbers in Different Bases: Symmetries and a Conjecture. EXPERIMENTAL MATHEMATICS, 26(2), 197-209 [10.1080/10586458.2016.1149125].
On Numbers in Different Bases: Symmetries and a Conjecture
FALCOLINI, Corrado
;
2017-01-01
Abstract
Any number may be written in many different ways, using different strings in different bases. In few, very special cases, a symmetry emerges which is usually hidden beneath the surface: 230164 and 164230 are both equal to 54284 in base ten. This article analyzes the solution set to the (constrained) Diophantine equation that implements such symmetry, culminating in a conjecture on the number of solutions of the equation.File in questo prodotto:
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