# Got a bijection?

$\large\sum _{ i=1 }^{ n }{ \left\lfloor \frac { A }{ B } i \right\rfloor } +\sum _{ j=1 }^{ m }{ \left\lfloor \frac { B }{ A } j \right\rfloor } = f(n)f(m)$

Let $A,B$ be odd natural numbers that are relatively prime, and let $n= \frac { B-1 }{ 2 }$, $m=\frac { A-1 }{ 2 }$ such that the equation above is fulfilled. If $f$ is a linear function with $f(1) > 0$, what is the sum of the coefficients of $f(x)$?

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