Find all units modulo 24 For each unit find its multiplicati

Find all units modulo 24. For each unit find its multiplicative inverse. Compute the multiplicative inverse of 43 modulo 101. Find all solutions x belongs to Z to the system of congruences x 0 mod 2 x 2 mod 3 x 3 mod 5.

Solution

note : only one question allowed per submission

Units modulo 24 are ={1,5,7,11,13,17,19,23}

Sine for each numbers we have x^2 = 1 mod 24, so each element is its own inverse

hence

{1,5,7,11,13,17,19,23} are the individual inverses of each above element