I am reading this with very little maths knowledge (since university 15 years ago) and I found this confusing:
"The multiplicative group of integers modulo n that we saw above gets more interesting when you consider a composite number such as 15 which has factors of 3 and 5. Repeated multiplication by 2 will never produce a multiple of 3 or 5 and this time there are only 8 numbers, {1,2,4,7,8,11,13,14} less than 15 that are not multiples of 3 or 5."
I understood the earlier example of "mod 3" because you only have {1,2} but then it becomes a lot more complicated but there's no explanation of it. Multiplying by 2 repeatedly under mod 15 only yields {1,2,4,8}.
After writing this, I saw you explained it a bit later in the document, so perhaps a note to that effect would help other readers.
"The multiplicative group of integers modulo n that we saw above gets more interesting when you consider a composite number such as 15 which has factors of 3 and 5. Repeated multiplication by 2 will never produce a multiple of 3 or 5 and this time there are only 8 numbers, {1,2,4,7,8,11,13,14} less than 15 that are not multiples of 3 or 5."
I understood the earlier example of "mod 3" because you only have {1,2} but then it becomes a lot more complicated but there's no explanation of it. Multiplying by 2 repeatedly under mod 15 only yields {1,2,4,8}.
After writing this, I saw you explained it a bit later in the document, so perhaps a note to that effect would help other readers.