7ai for the case n 5 m 3 sigma5k 01k5 5k5k3 1degree5553

(for the case n = 5, m = 3): sigma^5_k = 0(-1)^k(5 5-k)(5-k)^3 = (-1)degree(5,5)5^3 + (-1)^1(5, 4)4^3 + (- +(-1)^3(5, 2)2^3 + (-1)^4(5, 1)1^3 + = 125 - 5(64) + 10(27) - 10(8) + (i)2!S(7,2) (ii) (5, 2)[2!S(7, 2)] (iii) 3!s(7, 3) (iv) (5, 3)[3!S(7, 3)] (v) 4!S(7, 4) (vi) (5, 4)[4!S(7, 4)] (n, k)[k!S(m, k)] For each r Element R there is at least one a Element R such that a^5 -2a^2 +a-r=polynomial x^5 - 2x^2 + x - r has odd degree and real coefficients. Co However. f (0) = 0 = f (1). so f is not one-to-one.

Solution

I think S stands for permutations or combinations here.