I'm having a hard time understanding modular numbers and aritmetic.

If I have

, then

where

is an integer. So if I want to find 23 in

, I write

which should turn out to be 11 right? So 23 is equal to 11 in

.

So if I want to find:

I need to find r such that:

where b is an integer and r is the smallest possible positve number satisfying the equation. Is this correct? 26 hours would bring us to 2 o-clock since 2 is the smallest positive integer such that

where

is an integer. So here,

.

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