The q-Integers And The Mersenne Numbers

Here we will show that the q-integers, the q-analogue of the integers that we can findin the q-calculus, are forming an additive group having a generalized sum similar to the sum ofthe Tsallis q-entropies of independent systems. The symmetric form of q-integers will bestudied too. We will see that these numbers are linked to the Kaniadakis \kappa-calculus. Inthe article, a final discussion will be devoted to the link of the q-integers to the Mersennenumbers. Besides the discussion of the previously mentioned numbers, the general aim of thepaper is that of popularizing the existence of the q-calculus.