My car's odometer recently passed 111,111 -- which out of curiosity I quickly factored as 3*7*11*13*37. Which got me wondering, What is known in general about the factorization of S(n,k) = 1 + n + n^2 + . . . + n^(k-1) ??? Of course S(n,k) = (n^k - 1) / (n - 1) = Prod r=1 to k-1 of (n - w^r), where w is a primitive kth root of unity. And conjugate pairs can be grouped together to get the product of just real factors: S(n,k) = fac(n,k) * Prod r=1 to [(k-1)/2] of (n^2 - 2 cos(2pi*r/k) + 1) where fac(n,k) = n+1 if k is even, = 1 if k is odd. But this doesn't seem to help much. Is this problem more solvable for n a prime? Are there asymptotics for the number of prime factors, their size, or their exponents? --Dan