Quants functions

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1.N(x) is a function defined on the set {0,1,2,3,...100} such that N(x+1)=N(x)-N(x-1). For how many values of x other than 50 is the relation f(x)=f(50) true? 2.A function f is defined such that f(n+2)=2*f(n+1)-f(n) for all integer values of ...
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1.N(x) is a function defined on the set {0,1,2,3,...100} such that N(x+1)=N(x)-N(x-1). For how many values of x other than 50 is the relation f(x)=f(50) true?

2.A function f is defined such that f(n+2)=2*f(n+1)-f(n) for all integer values of n. If f(11)=17 and f(17)=35, then find f(35)


How to solve these kind of problems? any generalised method?

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