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2012 ToT Fall Senior O p4 no fo prime divisors, finite, C(a+b)=C(a)+C(b)

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March 22, 2020
number theoryprimeDivisors

Problem Statement

Let C(n)C(n) be the number of prime divisors of a positive integer nn. (a) Consider set SS of all pairs of positive integers (a,b)(a, b) such that a≠ba \ne b and C(a+b)=C(a)+C(b)C(a + b) = C(a) + C(b). Is SS finite or infinite? (b) Define S′S' as a subset of S consisting of the pairs (a,b)(a, b) such that C(a+b)>1000C(a+b) > 1000. Is S′S' finite or infinite?
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