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Remainder of 18n+17 mod 1920 - Iran First Round 2018, P6

Source:

March 6, 2021
number theorymodular arithmetic

Problem Statement

Let nn be the smallest positive integer such that the remainder of 3n+453n+45, when divided by 10601060, is 1616. Find the remainder of 18n+1718n+17 upon division by 19201920.
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