Hi this is a part of my math homework for the chinese new year hols- it's a reading scheme on "A Few Words about Proofs" could sbd help me plzplzplz?? tysm x(
Q1. Prove that X^(2)-1 is always divisible by 4 where X is an odd integer.
Solution 1: Since X is an odd integer, so the remainder when X is divided by 4 is either 1 or 3. If the remainder is 1, the remainder when X^2 is divided by 4 is 1x1=1. Hence X^(2)-1 is divisible by 4.
If the remainder is 3, the remainder when X^2 is divided by 4 is 3x3=9. Hence the remainder when X^(2)-1 is divided by 4 is the same as that of (9-1)/4 which is 0. Therefore, X^(2)-1 is always divisible by 4 where X is an odd integer.
Your comments on solution 1:
Your Solution:
Well actually, I have no idea what solution 1 is trying to say, but i can't really say that in the "comments". (really great start for the first q in the whole worksheet-.-) Should i just say how can (9-1)/4 even be 0?? Anybody have a solution plzzz thanks
:*Ellis
Q1. Prove that X^(2)-1 is always divisible by 4 where X is an odd integer.
Solution 1: Since X is an odd integer, so the remainder when X is divided by 4 is either 1 or 3. If the remainder is 1, the remainder when X^2 is divided by 4 is 1x1=1. Hence X^(2)-1 is divisible by 4.
If the remainder is 3, the remainder when X^2 is divided by 4 is 3x3=9. Hence the remainder when X^(2)-1 is divided by 4 is the same as that of (9-1)/4 which is 0. Therefore, X^(2)-1 is always divisible by 4 where X is an odd integer.
Your comments on solution 1:
Your Solution:
Well actually, I have no idea what solution 1 is trying to say, but i can't really say that in the "comments". (really great start for the first q in the whole worksheet-.-) Should i just say how can (9-1)/4 even be 0?? Anybody have a solution plzzz thanks
:*Ellis