Answer to Question #150247 in Statistics and Probability for Amir

Question

Leta,b,c,x,y, and z be positive integers such that (a^2−2) / x = (b^2−37) / y = (c^2−41) / z = a+b+c. Let S=a+b+c+x+y+z. Compute the sum of all possible values of S.

Answer 1

Using broot force (check all positive integers from 0 to 1000 for each a, b, c) we compute that threre are two solutions:

a = 32, b = 16, c = 25, x = 14, y = 3, z = 8 and S = 98

a = 32, b = 89, c = 25, x = 7, y = 54, z = 4 and S = 211

Hence, the sum of all possible values of S would be 211+98 = 309.