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Old 2015-09-16, 13:22   #45
wildrabbitt
 
Jul 2014

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I've finished the proof of lemma 1 in my head. I will write it down now and post it as soon as.
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Old 2015-09-16, 13:39   #46
LaurV
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Can you \TeX? It saves time, easy to make corrections, easy for other to read or copy, etc... You can preview interactively to see if it appears as you intended. Just suggestion, no harm intended. No harm if you can't.

edit: induction?

Last fiddled with by LaurV on 2015-09-16 at 13:44 Reason: s/save/saves/
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Old 2015-09-16, 14:36   #47
wildrabbitt
 
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If you'll give me a couple of days max to prove my lemma I'll learn to TEX.

Deal?
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Old 2015-09-16, 14:42   #48
wildrabbitt
 
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Actually I think I do have it. Hang on.
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Old 2015-09-16, 15:47   #49
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Quote:
Originally Posted by wildrabbitt View Post
If you'll give me a couple of days max to prove my lemma I'll learn to TEX.
What's the rush? Take your time.
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Old 2015-09-16, 20:03   #50
wildrabbitt
 
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Okay. Thanks for waiting. I've finished the proof. The rest of the whole proof is easy. I am certain I can show

that all the series of reciprocals formed from any set of positive integers with no a.p's longer than 2 converges and is bounded
above by the number 6.

Here's the beginning : I understand it's quite hard work reading a long proof. I hope some of you will make the effort because it's correct.

Haven't had time to learn TEX but I guess you're okay about that (for now) and I can only post two pages at once.

http://www.mersenneforum.org/attachm...1&d=1442433731

http://www.mersenneforum.org/attachm...1&d=1442433740
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Old 2015-09-16, 20:09   #51
wildrabbitt
 
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This might help to visualise the issue :


http://www.mersenneforum.org/attachm...1&d=1442434165
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Old 2015-09-16, 20:17   #52
wildrabbitt
 
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Pages 3 and 4 :

http://www.mersenneforum.org/attachm...1&d=1442434602

http://www.mersenneforum.org/attachm...1&d=1442434602
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Old 2015-09-16, 20:41   #53
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Quote:
Originally Posted by R.D. Silverman View Post
Actually, for a non-native speaker, your English is SUPERB.
This is one of the nicest things RDS has said all year. Congrats, LaurV!
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Old 2015-09-17, 01:55   #54
LaurV
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Quote:
Originally Posted by VBCurtis View Post
This is one of the nicest things RDS has said all year. Congrats, LaurV!
Quote:
Originally Posted by R.D. Silverman View Post
Actually, for a non-native speaker, your English is SUPERB.
Yeah, thanks a lot Mr. Silverman, unfortunately it is not true, and also unfortunately, it is not about math...
Dreaming of the day when you will say "your number theory is satisfactory", haha, most probably never
/end of offtopic

Last fiddled with by LaurV on 2015-09-17 at 01:58
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Old 2015-09-17, 17:13   #55
wildrabbitt
 
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I feel it's my duty in case the lack of responses so far isn't because everyone's lost interest, to post the rest of
the proof of the lemma.

There's still one more to page to come after these and after that there's a little more about the density of the terms of
the sequence of positive integers. I'll post the rest of this lemma's proof but I won't post anymore after that unless people
say they want me to.


http://www.mersenneforum.org/attachm...1&d=1442509786


http://www.mersenneforum.org/attachm...1&d=1442509786
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