# Day 1: A Partridge in a Number Tree

**Number Theory**Level 5

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:

- It is a square number,
- 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,
- 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.