Hi everyone, I have a problem in the following modular arithmetic operation
1/2*(x-4)(x-5) = 4(x-4)(x-5) (mod 7) ("=" means congruent in this expression)
The Attempt at a Solution
I am completely lost on how the operation is valid. If the coefficient is an integer between 0 to 6 then I can easily find its inverse using euclid extended algorithm but the problem here is that the coefficient is 1/2, a rational number. Any help on this problem will be greatly appreciated!