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s(n) \ge n , binomial remainder

Source: 2015 Saudi Arabia GMO TST II p4

July 26, 2020
Binomialremaindernumber theorycombinatoricsinequalities

Problem Statement

For each positive integer nn, define s(n)=∑k=0nrks(n) =\sum_{k=0}^n r_k, where rkr_k is the remainder when (nk)n \choose k is divided by 33. Find all positive integers nn such that s(n)≥ns(n) \ge n.
Malik Talbi
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