Question 32879
 Since f(a)=f(b)=f(c)=f(d)=8, assume
 f(x) = g(x) (x-a)(x-b)(x-c)(x-d) + 8, where g(x) is  monic poly. in Z[x]

 If  f(k) = 3 , then g(k) (k-a)(k-b)(k-c)(k-d) =  -5.
 But 5 is a prime and g(k) is nan integer, a,b,c,d are distict.
 Hence, at least two among (k-a),(k-b),(k-c),(k-d) would be equal to
 1 or -1 , this is impossible.

 Kenny