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a_{100},a_{101},a_{102},... form arithmetic sequence , a_n is divisible by n

Source: 2010 Swedish Mathematical Competition p4

April 30, 2021
arithmetic sequencenumber theory

Problem Statement

We create a sequence by setting a1=2010a_1 = 2010 and requiring that an−an−1≤na_n-a_{n-1}\leq n and ana_n is also divisible by nn. Show that a100,a101,a102,…a_{100},a_{101},a_{102},\dots form an arithmetic sequence.
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