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March 20th, 2018, 06:57 AM   #1
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Help me prove this and I'll give you money and stuff

Hi I just need help with advice on proving this conjecture I came up with; it is completely meaningless, so you are welcome ask why should we care etc., etc., but if you do give a proof I deem acceptable I will give that lucky guy/girl \$10.

I'm just assuming anyone else that spends their time doing this will be pleased about that; if not, I hope you are not offended by the size of the prize pool.
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Last edited by skipjack; March 21st, 2018 at 05:08 AM.
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March 20th, 2018, 08:49 AM   #2
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Sorry prize already been won

proof from Marcin Augustynowicz:

If p does not divide k you have two possibilites.

Either the prime exponent of p in n is 1, and then in the thing in brackets it is the same or it is greater or equal than 2, but the prime exponent of the formula in brackets is exactly two.

If p divides k let a and b be the exponents of p in prime factorisation of k and n respectively.

We know that k^3|n, so b>=3a, but the prime exponent of the formula in brackets is always less than or equal to a+2 and b>=3a>=a+2.

So in either case for any p the prime exponent of n is greater or equal than that of a bracket thing, and that's why the divisibility holds. And looking at this proof it is easy to see that generally the converse does not hold.
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March 20th, 2018, 09:03 AM   #3
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...but if you do give a proof I deem acceptable I will give that lucky guy/girl \$10.
......rumor has it you already bet $100 you could come
up with a proof in the near future......
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Last edited by skipjack; March 21st, 2018 at 05:10 AM.
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March 20th, 2018, 09:19 AM   #4
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Well im sure i would have come up "a" proof

Well indeed I thought I would have one within the week or so and didn't anticipate on Marcin immediately telling me how "easy" it is and providing a proof after prompting to do so, if I had known that one was lurking in the facebook group I wouldn't have offered up the \$10. I'm sure Marcin deserves it; I would just prefer it if I keep that money for my food budget, I get quite low on carbs without "mi goreng".

Last edited by skipjack; March 21st, 2018 at 05:13 AM.
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March 20th, 2018, 09:23 AM   #5
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...trade you my hockey stick for your boomerang.
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March 20th, 2018, 09:43 AM   #6
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Boomerang

I'm sorry I don't have one and for historical accuracy they absolutely do not return upon throwing them and were never meant to, the aboriginals would simply hurl them at whatever animal they wished to be dead and they would travel in a linear path directly at said animal.
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March 20th, 2018, 09:49 AM   #7
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Looks like you're right:
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March 20th, 2018, 10:02 AM   #8
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At least croc dundee is fading as an icon

well i don't mind too much what people use as associations to various cultures but I just hope that the American perception of Australia still isn't some backward knife wielding moron dressed like circus performer.

Some other guy tried to bring it back and that's why God made a sting ray stab him.
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March 20th, 2018, 07:50 PM   #9
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Rumour has it?

what... what did you mean by that exactly I'm not sure I like your sarcasm dennis
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March 20th, 2018, 07:56 PM   #10
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Quote:
Originally Posted by Adam Ledger View Post
well i don't mind too much what people use as associations to various cultures but I just hope that the American perception of Australia still isn't some backward knife wielding moron dressed like circus performer.
Bahaha. Oh I'm sure they do. Not much to be proud of here down under I'm afraid Mr. Ledger. A culture-less babble of ignorance.
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