B A question regarding multiples of 3

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1. Dec 20, 2016

guifb99

Why doesn't any odd multiple of 3 can give "24-1(x2-1)=y" as a result (y) a natural number? Obviously no even number will make "y" a natural number, but all of the odd numbers do, but odd multiples of 3 (3, 9, 15, 21, 27...).

x=1⇒y=0
x=3⇒y=1/3
x=5⇒y=1
x=7⇒y=2
x=9⇒y=10/3
x=11⇒y=5
x=13⇒y=7
x=15⇒y=28/3
x=17⇒y=12
x=19⇒y=15
x=21⇒y=55/3
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.
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Last edited: Dec 20, 2016
2. Dec 20, 2016

Staff: Mentor

Can you explain this better perhaps by using an example?

3. Dec 20, 2016

guifb99

I'm sorry, I typed it wrongly, it's not "1/2", it's "1/24".

4. Dec 20, 2016

Staff: Mentor

Okay, but can you explain this better perhaps by using an example?

Is this a homework assignment?

5. Dec 20, 2016

guifb99

There, now I think it's WAY better understandable. I'm sorry. Lol

6. Dec 20, 2016

TeethWhitener

You mean, why does the expression:
$$\frac{1}{24}(x^2-1)$$
not return an integer when $x$ is an odd multiple of 3? Think about what "odd multiple of 3" means mathematically and substitute that for $x$ in the expression above to see what you get.

7. Dec 20, 2016

Staff: Mentor

Can x2-1 be divisible by 3 if x is divisible by 3?