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# Pre-RMO 2014/17

For a natural number $$b$$, let $$N(b)$$ denote the number of natural numbers $$a$$ for which the equation $$x^2 + ax + b = 0$$ has integer roots. What is the smallest value of $$b$$ for which $$N(b) =6$$?

This note is part of the set Pre-RMO 2014

Note by Pranshu Gaba
2 years, 3 months ago

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The question becomes in finding the smallest positive integer which has 12 factors(negative). · 2 years, 3 months ago

We must also check the smallest integer with 11 factors, for example $$2^{10}$$, even that will give $$N(b) = 6$$. · 2 years, 3 months ago