What is the smallest integer n that satisfies both of the following equations, in which p and q
are positive integers?
n = p2 + p
n = q2 + q + 2014 Choose the correct choice from the following answers:
A) 2024  B) 2034  C) 2056  D) 2070  E) 2196
The term 2014 in the second equation suggests trying small numbers for q, and a   little experimentation with p close to the square root of 2014 and n = p(p + 1) leads fairly   quickly to q = 7, giving n = 2070, which is (45)(46)   correct answer 2070
<result>D</result>
What is the smallest integer n that satisfies both of the following equations, in which p and q
are positive integers?
n = p2 + p
n = q2 + q + 2014