Ingham Divisor Problem with Square-Free Numbers / Goryashin D.V. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2011. № 3. P. 52-55 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].

For the number N(x) of solutions to the equation aq - bc = 1 in positive integers a,b,c and square-free numbers q satisfying the condition aq ≤ x the asymptotic formula

N(x)=Σn≤x2ω(n)τ(n-1) = ξ0 x ln2x + ξ1 x lnx + ξ2 x + O(x5/6+ε)
is obtained for any ε > 0, where ξ0, ξ1,ξ2 are constants.

Key words: Ingham divisor problem, binary additive problems, asymptotics for the number of solutions.

№ 3/2011