2. b :
3. n :
4. b
n 
5. a+b
n = ((a+bn) 
n)n+((a+bn) rem n)
6. a = (a
n)n+(a rem n)
7. ((a+b
n) rem n) n
8. (a rem n)
n
((a+bn) rem n) = (a rem n)
n
n = ((a+bn) n)n+((a+bn) rem n)
n)n+(a rem n)
n) rem n) n
n
((a+bn) rem n) = (a rem n)| By: |
Thm*  k:, r1,r2:k, q1,q2: . q1k+r1 = q2k+r2   q1 = q2 & r1 = r2
on [ ((a n)+b)n+(a rem n) = ((a+bn) n)n+((a+bn) rem n) ] |
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