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concatenating no, a_1 = n^2011, a_i is sum of the digits of a_{i-1}, a_4 ?

Source: Norwegian Mathematical Olympiad 2011 - Abel Competition p1

September 4, 2019
number theorysum of digitsSequence

Problem Statement

Let nn be the number that is produced by concatenating the numbers 1,2,...,40221, 2,... , 4022, that is, n=1234567891011...40214022n = 1234567891011...40214022. a. Show that nn is divisible by 33. b. Let a1=n2011a_1 = n^{2011}, and let aia_i be the sum of the digits of ai−1a_{i-1} for i>1i > 1. Find a4a_4
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