Heres the question, I have tried to construct such a function, but I keep having trouble making it so both conditions are met, I seem to only be able to manufacture a function that works for one of the conditions, or the other, but not both simultaneous. I dont need a full blown answer, but I would definantly like some guidence as to where to go next:

If

are distinct numbers, find a polynomial function

of degree

which is

at

and

at

for

.

The question also gives a hint:

The product of all

for

, is

at

if

.

Thank you for any help on this question that anybody can give.