# My objective is linear

Number Theory Level 5

$$a$$ and $$b$$ are positive integers such that

$\begin{cases} 7b-11a \leq 1000 \\ ab + a^2= 1+b^2. \\ \end{cases}$

What is the largest possible value of $$7b-11a$$?

Details and assumptions

There is no restriction that $$a$$ or $$b$$ must be less than 1000.

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