Diophantine Equations With Positive Solutions ----------- --------- ---- -------- --------- You are to find a strictly positive integral solution (x,y) to A*x + B*y = C given that A, B, C are strictly positive integers. Polynomial equations with integer coefficients in which only integer solutions are sought are called Diophantine equations, so we are asking for positive solutions of one of the simplest Diophantine equations. Input ----- For each of several test cases, a single line of the form: A B C where 10 <= A,B <= 1,000 10 <= C <= 1,000,000 Input ends with an end of file. Output ------ For each test case, one line of the form A * x + B * y = C where all the letters are replaced by non-zero positive integers so as to make the equation true. The integers replacing A, B, C are taken from the test case input line. You must find the solution values of x and y. Input will be such that there is a unique solution. Sample Input ------ ----- 10 25 100 29 17 300 33 66 99 128 241 34647 128 241 34648 128 241 34649 113 197 21952 113 197 21953 113 197 21954 113 197 21955 113 197 30001 Sample Output ------ ------ 10 * 5 + 25 * 2 = 100 29 * 8 + 17 * 4 = 300 33 * 1 + 66 * 1 = 99 128 * 137 + 241 * 71 = 34647 128 * 105 + 241 * 88 = 34648 128 * 73 + 241 * 105 = 34649 113 * 67 + 197 * 73 = 21952 113 * 135 + 197 * 34 = 21953 113 * 6 + 197 * 108 = 21954 113 * 74 + 197 * 69 = 21955 113 * 133 + 197 * 76 = 30001 File: positive.txt Author: Shai Simonson Editor: Bob Walton Date: Thu Oct 4 20:12:03 EDT 2018 The authors have placed this file in the public domain; they make no warranty and accept no liability for this file.