Little math problems September 2018
09-26-2018, 03:55 PM (This post was last modified: 09-26-2018 04:00 PM by pier4r.)
Post: #13
 pier4r Senior Member Posts: 2,108 Joined: Nov 2014
RE: Little math problems September 2018
1) albert commenting his own post.

2) Sorry I thought it was not needed. I find all the effort put into solutions neat. Of course even further explorations are appreciated. I find that good(great/outstanding/etc..) contributions are good even without comments. A good contribution is not good only when commented.

3) I guess I claimed too early something I (and the other guys at the math jam) didn't test enough. At the math jam I observed (the other guy did it too independently and then we confronted the solutions n1) the following:
Code:
 I forgot the spoiler alert 2^2 + 2^2 = 8 = 2^3 2^3 + 2^3 = 16 = 2^4 = (2^2)^2 2^8 + 2^8 = 2*2^8 = 2^9 = (2^3)^3  2^9 + 2^9 = 2*2^9 = 2^10 = (2^5)^2  so we quickly settled on (we didn't test much) odd powers of two as exponent. 2^32 + 2^32 = 2*2^32 = 2^33 = (2^11)^3 2^33 + 2^33 = 2*2^33 = 2^34 = (2^17)^2  2^128 + 2^128 = 2*2^128 = 2^129 = (2^43)^3 2^129 + 2^129 = 2*2^129 = 2^130 = (2^65)^2 2^512 + 2^512 = 2*2^512 = 2^513 = (2^171)^3 2^513 + 2^513 = 2*2^513 = 2^514 = (2^257)^2 2^(2^(2k+1)) + 2^(2^(2k+1)) = 2*2^(2^(2k+1)) = 2^(2^(2k+1)+1) Now indeed we didn't prove that 2^(2k+1)+1 is always a multiple of 3. 2^(2^(2k+1)+1) + 2^(2^(2k+1)+1) = 2*2^(2^(2k+1)+1) = 2^(2^(2k+1)+2) While 2^(2k+1)+2 , still we didn't really check at the time, is a multiple of 2. If 2^(2k+1)+1 is a multiple of 3 always, then there is a family of solutions. I will check later.

n1: the idea at the math jam is to work on a problem on your own, then share the solutions and double check them. If everyone is stuck, then brainstorming together.

update: what the solutions in this threads shows is that there seems to be other fitting numbers as well. We had only pen + paper in a bar at the mathjam so we didn't stay on the problem too long.

Wikis are great, Contribute :)
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 Messages In This Thread Little math problems September 2018 - pier4r - 09-20-2018, 11:21 AM RE: Little math problems September 2018 - Thomas Klemm - 09-20-2018, 12:54 PM RE: Little math problems September 2018 - Albert Chan - 09-20-2018, 01:03 PM RE: Little math problems September 2018 - Albert Chan - 09-20-2018, 02:37 PM RE: Little math problems September 2018 - Albert Chan - 09-25-2018, 02:46 AM RE: Little math problems September 2018 - ijabbott - 09-20-2018, 04:55 PM RE: Little math problems September 2018 - Albert Chan - 09-20-2018, 05:22 PM RE: Little math problems September 2018 - Valentin Albillo - 09-24-2018, 12:53 AM RE: Little math problems September 2018 - Albert Chan - 09-24-2018, 12:18 PM RE: Little math problems September 2018 - Valentin Albillo - 09-25-2018, 12:48 AM RE: Little math problems September 2018 - Albert Chan - 09-28-2018, 04:51 PM RE: Little math problems September 2018 - pier4r - 09-25-2018, 10:56 AM RE: Little math problems September 2018 - Valentin Albillo - 09-25-2018, 04:09 PM RE: Little math problems September 2018 - pier4r - 09-26-2018 03:55 PM RE: Little math problems September 2018 - Valentin Albillo - 09-26-2018, 08:13 PM RE: Little math problems September 2018 - Albert Chan - 09-26-2018, 10:20 PM RE: Little math problems September 2018 - pier4r - 09-28-2018, 01:36 PM RE: Little math problems September 2018 - pier4r - 09-27-2018, 10:42 PM RE: Little math problems September 2018 - Albert Chan - 09-27-2018, 11:45 PM

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