(a) Solve Archimedes' Cattle a symbolic algebra program. (b) The Cattle a second part in

Chapter 10, Problem T1

(choose chapter or problem)

(a) Solve Archimedes' Cattle a symbolic algebra program. (b) The Cattle a second part in which two additional conditions are imposed. The first of these states that When the white bulls mingled their number with the black, they stood firm, equal in depth and breadth. This requires that be a square number, that is, 1, 4, 9, 16, 25, and so on. Show that this requires that the values of k in Eq. 4 be restricted as follows: and find the smallest total number of cattle that satisfies this second condition. Remark The second condition imposed in the second part of the Cattle that When the yellow and the dappled bulls were gathered into one herd, they stood in such a manner that their number, beginning from one, grew slowly greater til it completed a triangular figure. This requires that the quantity be a triangular numberthat is, a number of the form , , , . This final part of the problem was not completely solved until 1965 when all 206,545 digits of the smallest number of cattle that satisfies this condition were found using a computer.