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In this paper we give some new consequences that follow from our formula forincrements of the Hardy-Littlewood integral. The main of these ones are$\mathcal{T}_1$ and $\mathcal{T}_2$ equivalents of the Fermat-Wiles theorem.

Jacob's ladders, almost linear increments of the Hardy-Littlewood  integral (1918) and their relation to the Titchmarsh's sums (1943) and the  Fermat-Wiles theorem