Question

10. A natural number n is called attainable if there exists non-negative integers a and b such that n - 5a + 8b. Otherwise, n is called unattainable. Construct an 9 x 6 matrix whose rows are indexed by the integers between 0 and 8 and whose columns are indexed by the integers between 0 and 5 whose (x, y)-th entry equals 5x + 8y for any 0 < r < 8 and (a) Mark down all the attainable numbers that are strictly less than 40 in your array. (b) For any 0-x-8. 0 y 5, prove that the (x, y)-th entry and the (8-2, 5-y)-th entry add up to 80. strictly less than 40. How many numbers less than 40 are unattainable? attainable. (c) Using the previous two parts, determine the number of attainable integers that are (d) Prove that 27 is the largest unattainable integer and that every integer n 2 28 is

Answer 1

回 in pnt (a) se unattainal 39 345 and all ether nunen a punt in Mente pro red