| fac(i - j) * j * fac(j - 1) = fac(j) * fac(i - j), 0 < i, 0 < j, j ≤ i, 0 ≤ j, 0 ≤ i ⊦ i * fac(i - 1) / (fac(i - j) * fac(j - 1)) = j * fac(i) / (fac(i - j) * j * fac(j - 1)), fac(i - j) * j * fac(j - 1) | fac(i) |
0 < i, 0 < j, j ≤ i, 0 ≤ j, 0 ≤ i ⊦ i * fac(i - 1) / (fac(i - j) * fac(j - 1)) = j * fac(i) / (fac(j) * fac(i - j)), fac(j) * fac(i - j) | fac(i)