[SOLVED] larson 3.3.19b 1. The problem statement, all variables and given/known data What is the largest number N for which you can say that n^5-5n^3+4n is divisible by N for every positive integer N. EDIT: change the last N to n 2. Relevant equations 3. The attempt at a solution I have just been plugging in things for n and seeing what happens. If n=N-2,N-1,N,N +1,N+2, then n^5-5n^3+4n is divisible by N because -2,-1,0,1,2 are the roots of that equation. If n=N+3, we get that 120 = -120 must equal 0 mod N. So, N=3 is a lower bound. So N must be a factor of 120. Should I just keep keep plugging in numbers for n and setting them equal to 0 mod N? It seems like that will give me a solution but that won't prove that this particular N works for all values of n.