MathDB

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Part of 2016 Lusophon Mathematical Olympiad

Problems(1)

smallest no of distinct prime factors in product of 10 distinct coprime integers

Source: Lusophon 2016 CPLP P1

8/29/2018
Consider 1010 distinct positive integers that are all prime to each other (that is, there is no a prime factor common to all), but such that any two of them are not prime to each other. What is the smallest number of distinct prime factors that may appear in the product of 1010 numbers?
number theoryPrime factorProductcoprimepositive integers