# Algebra and little number theory

Algebra Level 4

If $$f:Q\rightarrow Q$$ satisfies

1) $$f\left( 1 \right) =2$$

2) For all $$x,y\in Q\quad f\left( xy \right) =f\left( x \right) f\left( y \right) -f\left( x+y \right) +1$$

Find $$f\left( 566 \right)$$ for $$f\left( x \right)$$.Now let answer as $$z$$.

Then find $$z$$ $$Mod$$ $$6$$.

Now let answer be $$c$$.

Then enter answer as $${ c }^{ 4 }$$.

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