1. Determine an inverse of a modulo m for a =6 and m = 11.  This is equivalent toanswering the question “_______ is the unique inverse of6 (mod 11) that is non-negative and <11.â€Â  Show your work following thesteps.
- Beside the inverse you identified in part a), identify twoother inverses of 6 (mod 11). Â
Hint:Â Â All of these inverses are congruent to eachother mod 11.
- Although the congruence can be solved using any of the inversesyou identified in parts a) and b), use the unique inverse of 6(mod 11) that you identified in part a), that is, thenon-negative inverse of 6 (mod 11) that is < 11, tosolve the following congruence.  Show yourwork.  6x ≡ 8(mod 11).
Determine if the congruence 6x ≡ 11(mod 8) hasa solution.
If there is a solution, identify a value forx.  If there is no solution, explain whynot.
