# Day 1: A Partridge in a Number Tree

A partridge sits in its tree. However, this is not a pear tree; it is a number tree! It rummages around until it finds a special type of number- let us call them partridge numbers.

Define a partridge number to be a number such that:

1. It is a square number,
2. It can be expressed in the form $$x^2y^2-x^2-y^2+2$$ where the positive integers $$x$$ and $$y$$ are not consecutive,
3. It cannot be expressed in the form $$x^2y^2-x^2-y^2+2$$ for any consecutive positive integers $$x$$ and $$y$$.

The first partridge number is between $$1$$ and $$2014$$. What number is it?

This problem is part of the set Advent Calendar 2014.

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