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max k nos in set {n+1, n+2, ... , n+16} which are coprime with n(n+17)

Source: 1985 Polish MO Finals p1

January 21, 2020
coprimenumber theorymaximum

Problem Statement

Find the largest kk such that for every positive integer nn we can find at least kk numbers in the set {n+1,n+2,...,n+16}\{n+1, n+2, ... , n+16\} which are coprime with n(n+17)n(n+17).
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