- #1
ajbiol
- 3
- 0
Hello all,
I was wondering if someone can explain to me a step in a proof given to me by my professor in regards to a modular operation theorem.
Addition theorem: Given three integers x, y, d (d > 0), (x+y)%d = (x%d + y%d) %d
Proof:
Let x = q(1)d + r(1) and y = q(2)d + r(2).
We have (x+y)%d = (q(1)d + r(1) + q(2)d + r(2)) %d
= (r(1) + r(2)) %d
Therefore: (x+y)%d = (x%d + y%d) %d
I don't get how my professor jumped from (q(1)d + r(1) + q(2)d + r(2))%d to (r(1) + r(2))%d.
Is there a specific reason for why we just ignore the product of q(1)d and q(2)d?
Thank you in advance.
I was wondering if someone can explain to me a step in a proof given to me by my professor in regards to a modular operation theorem.
Addition theorem: Given three integers x, y, d (d > 0), (x+y)%d = (x%d + y%d) %d
Proof:
Let x = q(1)d + r(1) and y = q(2)d + r(2).
We have (x+y)%d = (q(1)d + r(1) + q(2)d + r(2)) %d
= (r(1) + r(2)) %d
Therefore: (x+y)%d = (x%d + y%d) %d
I don't get how my professor jumped from (q(1)d + r(1) + q(2)d + r(2))%d to (r(1) + r(2))%d.
Is there a specific reason for why we just ignore the product of q(1)d and q(2)d?
Thank you in advance.