how do i prove given any integer X that X,X+2 or X+4 is always divisivle by 3?
>>7662724
think about what numbers are divisible by 3 and their relation to each other.
By way of contradiction, I'd wager
>>7662724
Given an integer X, we can consider its remainder when divided by 3. This remainder can only be 0, 1, or 2. That is, there exists an integer k such that X = 3k, X = 3k + 1, or X = 3k + 2.
Case 1: X = 3k
Then X is divisible by 3.
Case 2: X = 3k + 1
Then X + 2 = 3k + 3 = 3 (k + 1) is divisible by 3, as desired.
Case 3: X = 3k + 2
Then X + 4 = 3k + 6 = 3 (k + 2) is divisible by 3, as desired.
>>7662728
OP here
what you mean by contradiction? not english native :)
>>7662729
got it, thanks :D
>>7662730
Use a number that isn't a multiple of 3 to prove your point.
>>7662724
ins't it a trivial question?
What is [math]\sqrt{Love}[/math].
Bby don't hurt me.
Don't hurt me.
No more.
>>7662756
[math] O^{O^{O^{O^{O^{O^{O^{O^{O}}}}}}}} , O^{O^{O^{O^{O^{O}}}}} , A^{A} [/math]
3 numbers from all 3 congruence classes modulo 3.
QED
>>7662782
Zero is divisible by every nonzero integer. Have fun in remedial math.
>>7662782
>Statement is incorrect.
>QED
>0 is not divisible by 3
THE MORE YOU KNOW
>>7662804
>You didn't negate your existential qualifier. Not the contrapositive. No proof.
The fuck are you talking about. A counterexample is a counter proof. Because P implies Q is disproved by any not Q using any P. His problem is that his counterexample is wrong.
>>7662804
>Not the contrapositive
The contrapositive doesn't have anything to do with what he was trying to show
This is really easy by using induction anon
[math]x(x+2)(x+4) = x(x+1)(x+2)+ 3 x (x+2)[/math]
>>7662730
Look up "modular arithmetic."
Hint: X+4 is the same as X+1 (mod 3).
