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Quadratic with integer roots

Source: 2014 aime i #6

March 14, 2014

quadraticsconicsparabolaVietafunctionLaTeXnumber theory

Problem Statement

The graphs of

y=3(x-h)^2+j

and

y=2(x-h)^2+k

have

y

-intercepts of

2013

and

2014

, respectively, and each graph has two positive integer

x

-intercepts. Find

h