Lol, integers

Let Pk(a)P_k(a) denote the greatest integer n that can not be represented by the form ax+by=nax+by=n for at least 11 ordered pair (x,y) and a specific aa and kk (kk is defined below in "assumptions and details")

For example, the largest integer n that can't be represented by P4(5)=5x+9yP_4(5)=5x+9y is 31 since no integer values of x and y satisfy 31=5x+9y31=5x+9y

Find P2014(2015)P2013(2015P_{2014}(2015)-P_{2013}(2015)

Tip:

P2014(2015)=2015x+4029yP_{2014}(2015)=2015x+4029y

P2013(2015)=2015x+4028yP_{2013}(2015)=2015x+4028y

Assumptions and details

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

b>ab>a.

ba=kb-a=k

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

This is part of the set Trevor's Ten

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