Number theory · Repunits · Greatest common divisor · Divisibility · Decimal representation
Find the greatest common divisor of the two numbers
\[ \underbrace{11111111}_{8}, \qquad \underbrace{11\ldots11}_{100}, \]
written with eight and with one hundred digits \(1\), respectively.
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Serbian Municipal Competition 2003, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source