In: Advanced Math
1. Determine an inverse of a modulo m for a = 6 and m = 11. This is equivalent to answering the question “_______ is the unique inverse of 6 (mod 11) that is non-negative and < 11.” Show your work following the steps.
Hint: All of these inverses are congruent to each other mod 11.
Determine if the congruence 6x ≡ 11(mod 8) has a solution.
If there is a solution, identify a value for x. If there is no solution, explain why not.
(d)
Want to find the solution of the equation
Thus this congruence equation's solution doesnt not exist.
Another approach for not existence:
Since 6x - 8 k = 11,
Here 6x is an even number and 8k is also an even number , so is 6x - 8k, but right hand side, 11 is an odd number.
Since an odd number is not equal to any even number, hence this equation doesn't have solution.