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pmo problem 5

Source: PMO 2021

March 20, 2021
algebranumber theoryPMO

Problem Statement

A positive integer is called \emph{lucky} if it is divisible by 77, and the sum of its digits is also divisible by 77. Fix a positive integer nn. Show that there exists some lucky integer ll such that ∣n−l∣≤70\left|n - l\right| \leq 70.
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