The q-Integers and the Mersenne Numbers
10 Pages Posted: 11 Jun 2018
Date Written: May 23, 2018
Abstract
Here we will show that the q-integers, the q-analogue of the integers that we can find in the q-calculus, are forming an additive group having a generalized sum similar to the sum of the Tsallis q-entropies of independent systems. The symmetric form of q-integers will be studied too. We will see that these numbers are linked to the Kaniadakis \kappa-calculus. In the article, a final discussion will be devoted to the link of the q-integers to the Mersenne numbers. Besides the discussion of the previously mentioned numbers, the general aim of the paper is that of popularizing the existence of the q-calculus.
Keywords: q-calculus, q-integers, Tsallis q-entropy, Mersenne numbers
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