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Sum of digits of N and N+1

Source: PAMO 2007 Q1

December 10, 2013
modular arithmeticnumber theory unsolvednumber theory

Problem Statement

Find all natural numbers NN consisting of exactly 11121112 digits (in decimal notation) such that: (a) The sum of the digits of NN is divisible by 20002000; (b) The sum of the digits of N+1N+1 is divisible by 20002000; (c) 11 is a digit of NN.
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