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|a_k-a_{k-1}|

Source: 5-th Taiwanese Mathematical Olympiad 1996

January 12, 2007
number theory unsolvednumber theoryInteger sequence

Problem Statement

Dertemine integers a1,a2,...,a99=a0a_{1},a_{2},...,a_{99}=a_{0} satisfying ∣ak−ak−1∣≥1996|a_{k}-a_{k-1}|\geq 1996 for all k=1,2,...,99k=1,2,...,99, such that m=max⁡1≤k≤99∣ak−ak−1∣m=\max_{1\leq k\leq 99} |a_{k}-a_{k-1}| is minimum possible, and find the minimum value m∗m^{*} of mm.
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