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arith. seq: nCk, nC(k+1), nC(k+2), nC(k+3)

Source: Yugoslav TST 1998 P3

May 15, 2021
algebraSequence

Problem Statement

Prove that there are no positive integers nn and k≤nk\le n such that the numbers (nk),(nk+1),(nk+2),(nk+3)\binom nk,\binom n{k+1},\binom n{k+2},\binom n{k+3}in this order form an arithmetic progression.
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