4. For an integer n > 0, let hn denote the number of n-digit integers with two properties (1) each digit is odd, (2) each of the digits 1, 3, 5, 7, 9 occurs an odd number of times. (a) Find ho, h1, h2, h3, h4, h5. (b) Find hn in a closed form.

Find the number of 5-tuples (a, b, c, d, e) of positive odd integers that are solutions to the equation a+b+c+ d +e = 65.

prove the following using either direct or indirect proof  a. if a is an odd integer, then 5a^2-3a+5 is odd   b. if x+y is greater or equal to 2, then x is greater or equal to 1 or y is greater or equal to 1

Let M = 10 6 [:: -3 1 Find formulas for the entries of M", where n is a positive integer. Mn = ((-2)(7^n))+4^n 7^n-(4^n) (-2)(7^n-4^n) 7^n-(2(4^n))