Thread: Todays Quiz Question

Show that for any prime , the number is divisible by 24.

PS. If you get it don't post your answer right away.[/tex]

Not true for p= 2 or 3.

Divisible to produce an integer or any real number?

Originally Posted by river_rat

Show that for any prime > 3, the number is divisible by 24.

PS. If you get it don't post your answer right away.[/tex]

huh, i guess it does work.

cant prove it though, at least i cant be bothered to.

If , then so either or is divisible by 3. Also or are consecutive even integers, so their product is divisible by 8. Hence is divisible by .

Sorry, river_rat, can’t help posting my solution right away. I did PM my solution to you at first, but in view of the post above, I simply have to teach some lazy bugger here a lesson on how maths should be done.

To make up for it, I can post the next quiz question when everyone’s ready.

yeah well screw you too

Mod note

Jane, Jek, please keep it civil, there's nothing to gained by name-calling and the like.

Thank you

-G-

haha im reading the question and im thinking to myself that theres no way the first couple of primes makes sense unless you are not talking about whole numbers.

Next quiz question.

If is an integer not divisible by 5, prove that is divisible by 20.

[Note to dumb ass: 0 is divisible by all integers!]

Try n =0 or 1 or 2 smart ass!

See note to dumb ass above.

Mod note Jane, please try to remain civil. Nothing is gained by name-calling
-G-

Proof:



Since , we have 5 consecutive numbers {n-2, n-1, n, n+1, n+2} such that the middle one isn't divisible by 5, so one of the others must be. Therefore, .

Similarly, if , then one of {n-2, n-1, n+1} is divisible by 4. If , then . Either way, .

Since 4 and 5 are relatively prime, .

Very nicely done, MagiMaster!



By the way, when mathematicians write , they usually mean divides , not is divisible by . But I understand what you mean.

Originally Posted by JaneBennet

is divisible by 5. I did say that should not be divisible by 5. Are you blind, or just a moron?

And what is wrong with or ?

Lol, No but at 73 I'm fast heading towards both, something i'm sure your attititude will not let you live long enough to see!

Originally Posted by JaneBennet

Very nicely done, MagiMaster!



By the way, when mathematicians write , they usually mean divides , not is divisible by . But I understand what you mean.

Jane i absolutely love your avatar... it's almost.... theraputic.

@Jane, Oh. It's been a while since I've used that symbol, so I think I just wrote it backwards. :P

@Megabrain, I think you made the mistake of assuming 0 is not divisible by anything, when it's actually divisible by everything. (Another way of saying that is that any integer can be multiplied by something to get 0.)

Mod note I have split this thread, as requested. I offer abject apologies for mis-spelling in the new title - I cannot figure how to edit it,

Let be an integer not divisible by 7. Prove that is divisible by 56.