# Lol, integers

Let $$P_k(a)$$ denote the greatest integer n that can not be represented by the form $$ax+by=n$$ for at least $$1$$ ordered pair (x,y) and a specific $$a$$ and $$k$$ ($$k$$ is defined below in "assumptions and details")

For example, the largest integer n that can't be represented by $$P_4(5)=5x+9y$$ is 31 since no integer values of x and y satisfy $$31=5x+9y$$

Find $$P_{2014}(2015)-P_{2013}(2015$$)

Tip:

$$P_{2014}(2015)=2015x+4029y$$

$$P_{2013}(2015)=2015x+4028y$$

Assumptions and details

$$(a,b,x,y,n)\epsilon \Bbb{N}$$

$$b>a$$.

$$b-a=k$$

$$\text{gcd}(a,b)=1$$

This is part of the set Trevor's Ten

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