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sum of digits of m = n(2n-1) is equal to 2000.

Source: 2001 Cuba MO 2.3

September 15, 2024
number theorysum of digits

Problem Statement

Prove that there is no natural number n such that the sum of all the digits of the number m, where m=n(2nāˆ’1)m = n(2n-1) is equal to 20002000.
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