由 ---- 於 星期六 五月 10, 2003 11:02 pm
By interpolation formula,
f(x)
=0+3(x-0)(x-3)(x-7)(x-a)/(1-0)(1-3)(1-7)(1-a) + 4(x-0)(x-1)(x-7)(x-a)/(3-0)(3-1)(3-7)(3-a)+5(x-0)(x-1)(x-3)(x-a)/(7-0)(7-1)(7-3)(7-a) + b(x-0)(x-1)(x-3)(x-7)/(a-0)(a-1)(a-3)(a-7)
for f(a)=b
where a isn't 0,1,3,7
As not enough information is given, there are infinity polynomials satisfying.