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GCD of two numbers consisting of ones

Source: South African MO 2004 Q1

May 27, 2012
number theorygreatest common divisoralgorithmnumber theory unsolved

Problem Statement

Let a=1111…1111a=1111\dots1111 and b=1111…1111b=1111\dots1111 where aa has forty ones and bb has twelve ones. Determine the greatest common divisor of aa and bb.
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