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In this paper we obtain number of new equivalents of the Fermat-Wiles theoremthat are based on Jacob's ladders. The main of these is the $D$-equivalent thatis generated by the Dirichlet's $D(x)$-function.

Jacob's ladders, almost linear increments of the Hardy-Littlewood  integral (1918), the classical Dirichet's sum of divisors (1849) and their  relationship with the Fermat-Wiles theorem