  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.
