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# modular arithmetic watch

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1. how come u can cancel multiples if u r using a prime base...but not if u r using a composite one...e.g

ax=ay (mod p) where p is prime
then x=y (mod p)

but u could not do that if p were not prime??? why?
2. also can u say that for example 13=11 (mod 2)??
3. Because if it is prime, and u have
ab = 0 (mod p)
Then either a = 0 (mod p), or b = 0 (mod p)

For composite numbers, it doesnt work like that, for instance

2*4 = 0 (mod 8)
but neither 2 or 4 = 0 (mod 8).

The definition of a prime number is: if p is prime, then
p|ab implies p|a or p|b.
4. Also, if u have p is composite, then

ax = ay (mod p)
x = y (mod p) is only true if a and p are coprime.

Anyway, ive gotta go, bye.
5. (Original post by JamesF)
Also, if u have p is composite, then

ax = ay (mod p)
x = y (mod p) is only true if a and p are coprime.

Anyway, ive gotta go, bye.
so it can be possible if p is not prime as long as p is not a multiple of a?
is it a definition of modulra arithmetic that p is bigger than a????

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