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NT with sum of digits

Source: Italy MO 2023 P3

May 7, 2023
number theory

Problem Statement

Let s(n)s(n) denote the sum of the digits of nn. a) Do there exist distinct positive integers a,ba, b, such that 2023a+s(a)=2023b+s(b)2023a+s(a)=2023b+s(b)? b) Do there exist distinct positive integers a,ba, b, such that a+2023s(a)=b+2023s(b)a+2023s(a)=b+2023s(b)?
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