Question

the equation 166×56 =8590 is valid in some base b>=10 (that is, 1,6, 5,8 9,0 are digits in base b in the above equation). Find the sum of all possible values of b>=10 satisfying the equation

Answer 1

For checking equations in bases other than 10, generally, we convert the equation to base 10, taking the unknown base as x. Next, we reduce the equation, factorize the polynomial and solve for integer value of x.