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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