中六數學科問題

1)Let f(x) be a degree 3 polynomial,satisfying f(1)=f(2)=f(3)=0 and f(4)=1,what is f(x)?
2)Let f(x) be a degree 4 polynomial,and let g(x) be a degree 2 polynomial.Suppose that f(x) and g(x) give the same values at x=1,2,3,and f(4)=g(4)+12,f(5)=g(5)+24.Find a polynomial identity linking up f(x) and g(x).
3)When n is divided by 7,the remainder is 3.Find the n that is closest to 100
4)Let n be a positive integer.When it is divided by 13,17 and 19,the remainders are respectively 0,1,and 0.Find the least possible value of n.