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ways to choose 2 numbers with product multiple of 5 and difference 5

Source: V May Olympiad (Olimpiada de Mayo) 1999 L1 P1

September 17, 2022
number theoryalgebra

Problem Statement

Two integers between 11 and 100100 inclusive are chosen such that their difference is 77 and their product is a multiple of 55. In how many ways can this choice be made?
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