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binomials in arithmetic progression

Source: 1973 Hungary - Kürschák Competition p1

October 15, 2022
binomial coefficientsCombinationsalgebraarithmetic sequence

Problem Statement

For what positive integers n,kn, k (with k<nk < n) are the binomial coefficients (nk−1)   ,   (nk)   ,   (nk+1){n \choose k- 1} \,\,\, , \,\,\, {n \choose k} \,\,\, , \,\,\, {n \choose k + 1} three successive terms of an arithmetic progression?
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