Algebra and little number theory

Algebra Level 4

If f:QQf:Q\rightarrow Q satisfies

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

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

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

Then find zz ModMod 66.

Now let answer be cc.

Then enter answer as c4{ c }^{ 4 }.

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