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2020 AMC 10AProblem 24P21-25~8 minPrint
GCD & LCMModular ArithmeticOrganized listing / direct enumerationSet up the equation/formula and compute; no special trick needed

Let nn be the least positive integer greater than 10001000 for which gcd⁡(63,n+120)=21andgcd⁡(n+63,120)=60.\gcd(63, n+120) =21\quad \text{and} \quad \gcd(n+63, 120)=60. What is the sum of the digits of nn ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.