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Part of 2014 Tuymaada Olympiad
Problems(2)
Minimum number of remainders
Source: Tuymaada 2014, Day 1, Problem 1, Senior League
7/13/2014
Four consecutive three-digit numbers are divided respectively by four consecutive two-digit numbers. What minimum number of different remainders can be obtained? (A. Golovanov)
modular arithmeticnumber theorygreatest common divisorleast common multiplerelatively primenumber theory proposedTuymaada
Maximum number of primes who divide their sum
Source: Tuymaada 2014, Day 1, Problem 1, Junior League
7/12/2014
Given are three different primes. What maximum number of these primes can divide their sum?(A. Golovanov)
number theory unsolvednumber theoryTuymaada