At the 6:50 min mark of this video: https://courses.edx.org/courses/HarvardX/CS50x3/2015/courseware/c0986764d695405f9d995f43b7c10676/5194906ad75c4edb9ecd401df372b8f3/
here's a screen shot, too: http://imgur.com/XuU8a23 
Isn't 1 mod 924 = 1, because the remainder in 1/924 is 1
In the video he declares e = 5
and then says de = 1 mod m
and quickly says that number is 185.
But why? shouldn't de = 1, in order to satisfy de = 1 mod m? Instead de = 925 or 5 * 185.
I went out and did the set on Khan academy for modulo arithmetic just to brush up my memory, but even with that I still don't get it. I get what x mod y means, I've been using it in the code for my problem sets, but what I don't get is why 1 mod anything is not 1.
I'm sure I'm missing something here.
PS: I'm aware he explains the process more around the 15 min mark, but what I never see explained is why if 1 mod 924 = 1, why doesn't d*e have to equal 1, if it is meant to "satisfy the equation"