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2012 ToT Fall Junior O p2 subset with number of prime divisors

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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 n. (For example, C(10)=2,C(11)=1,C(12)=2C(10) = 2,C(11) = 1, C(12) = 2). Consider set S 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 set SS finite or infinite?
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