20150916, 13:22  #45 
Jul 2014
2·3^{2}·5^{2} Posts 
I've finished the proof of lemma 1 in my head. I will write it down now and post it as soon as.

20150916, 13:39  #46 
Romulan Interpreter
"name field"
Jun 2011
Thailand
3·23·149 Posts 
Can you ? 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 20150916 at 13:44 Reason: s/save/saves/ 
20150916, 14:36  #47 
Jul 2014
111000010_{2} Posts 
If you'll give me a couple of days max to prove my lemma I'll learn to TEX.
Deal? 
20150916, 14:42  #48 
Jul 2014
2·3^{2}·5^{2} Posts 
Actually I think I do have it. Hang on.

20150916, 15:47  #49 
Jun 2003
1010100111101_{2} Posts 

20150916, 20:03  #50 
Jul 2014
2×3^{2}×5^{2} Posts 
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 
20150916, 20:09  #51 
Jul 2014
1C2_{16} Posts 

20150916, 20:17  #52 
Jul 2014
2×3^{2}×5^{2} Posts 
Pages 3 and 4 :
http://www.mersenneforum.org/attachm...1&d=1442434602 http://www.mersenneforum.org/attachm...1&d=1442434602 
20150916, 20:41  #53 
"Curtis"
Feb 2005
Riverside, CA
1606_{16} Posts 

20150917, 01:55  #54  
Romulan Interpreter
"name field"
Jun 2011
Thailand
24051_{8} Posts 
Quote:
Quote:
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 20150917 at 01:58 

20150917, 17:13  #55 
Jul 2014
2×3^{2}×5^{2} Posts 
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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