MathDB

4

Part of 2010 Swedish Mathematical Competition

Problems(1)

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

Source: 2010 Swedish Mathematical Competition p4

4/30/2021
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.
arithmetic sequencenumber theory