Hello,

I don't know how far you've studied these things... Nevermind...

We want to show that

The cardinal of (Z/89Z)* is 88 because 89 is a prime integer.

The elements of (Z/89Z)* are the positive integers <89 and coprime with 89. Because 89 is prime, any integer <89 will be coprime with 89. Hence, 2 belongs to (Z/89Z)*.

We know that the order m of an element belonging to (Z/89Z)*, here 2, divides its cardinal, 88.

Hence,

m is such as :

is .

Now,

---->

QED.