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arXiv · 2108.13471

On the 2-adic valuation of (a^b-c^d)

Luca Onnis
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Abstract

In this paper will be proved an inequality regarding $v_2(a^{b}-c^{d})$. Using this formula it will be possible to have informations about the divisibility of 2 of this function without computing it. Then, will be studied the behavior of this function when it approaches infinity and there will be a lot of analogies with 2-adic integers. This result may be easily used on a calculator, to facilitate the analysis of the divisibility by 2 of this function for large values. Furthermore 2-adic valuation and in general 2-adic analysis is related to binary system, and every work related to it could have a lot of applications in informatics.

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Luca Onnis. 2021-08-30. On the 2-adic valuation of (a^b-c^d). https://arxiv.org/abs/2108.13471

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