Originally Posted by

**Wandering** Hi, I have just started learning the fundamentals of Number Theory and I'm having some trouble wrapping my head around a few steps that were presented in my textbook.

the first question contains a simplification of:

7x = 1(mod 8)

to

-x = 1(mod)

a side note states that this is possible because 7=-1(mod 8)

Now, if 7 were congruent to -1(mod 8), and since -1(mod 8) is congruent to -1 (this is what I gathered from their next step), would this imply that 7 is congruent to -1, and hence the next step simply replaces 7 with -1?