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

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

TopNewest@Ar Agarwal how is it 60?

Log in to reply

The question becomes in finding the smallest positive integer which has 12 factors(negative).

Log in to reply

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

Log in to reply

Answer is 60

Log in to reply