# An algebra problem by Dipa Parameswara

Algebra Level 3

$f(n+2)+7f(n+1)+10f(n)=0$ $f(0)=2$ $f(1)=-13$

If $f(100)$ can be expressed as $a(b-3)^{100}-c(102-d)^{100}$ where $$a> 0, b-3>0 , 102-d>0$$ and $$c<101$$, then what is the value of $$(b+c+d)^{a}$$?

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