20060219, 16:24  #12  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2×7^{2}×109 Posts 
Quote:
Paul 

20060219, 18:41  #13  
Jun 2005
Near Beetlegeuse
388_{10} Posts 
Quote:
Quote:
Or, alternatively, can you please define (6, 14, 50, ...etc) a little more precisely? I know a certain member of this forum who would describe "...etc" as "hand waving nonsense. So lacking in precision as to be mathematically useless". LOL Many thanks, Numbers 

20060219, 19:23  #14  
∂^{2}ω=0
Sep 2002
Repรบblica de California
2×5×1,163 Posts 
Quote:


20060219, 19:26  #15  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2×7^{2}×109 Posts 
Quote:
He claimed that numbers which are congruent to 2 mod 4 are the problem. He did not say that all numbers in that residue class lead to difficult problems, only that the other three residue classes mod 4 have trivial solutions. He did say that some, including 6, 14 and 50, do lead to difficult and, indeed, presently unsolved problems. Bob could and should have phrased himself much more clearly, IMO. Paul 

20060219, 19:27  #16 
Aug 2002
Buenos Aires, Argentina
54C_{16} Posts 
See the sequence at OEIS: http://www.research.att.com/~njas/sequences/A074981 : 6, 14, 34, 42, 50, 58, 62, 66, 70, 78, 82, 86, 90, 102, 110, 114, 130, 134, 158, 178, 182, 202, 206, 210, 226, 230, 238, 246, 254, 258, 266, 274, 278, 290, 302, 306, 310, 314, 322, 326, 330, 358, 374, 378, 390, 394, 398, 402, 410, 418, 422, 426, ...
According to that page it is conjectured that none of these numbers can be a difference of two powers. 
20060219, 19:48  #17 
Jun 2003
1,579 Posts 
What is the solution for the number=2 and 125. Anyone know one?
Are these all the numbers upto infinity or under 500? Citrix 
20060219, 20:48  #18 
Jun 2005
Near Beetlegeuse
110000100_{2} Posts 
Thank you, all three of you. Now it makes sense. And I note that none of you were able to define N (which is not a criticism, just a point that I will come back to).
What actually interested me about this problem is not a desire to solve it, but a conundrum that arises out of my suspicion that you would not in fact be able to define N. Now, let f(x) = x^a  y^b, so that the problem can be stated as: When does f(x) = N? The conjecture referred to in Alpertron's post says that f(x) never = N for N in A074981. For obvious reasons, A074981 is a finite representation of what is presumably an infinite sequence. So there are values of N that should be in the sequence that are not at OEIS, or any other list of the sequence. Let's say M is a number that should be in N, but is not on any recorded list of N. Joe Nobody finds that f(x) = M. Since no one can define N, how does Joe even prove that M is in N and that he has found a counterexample to the conjecture? You could probably get quite cute with your semantics and claim that since M should be in N, then Joe cant find that f(x) = M, but I'm sure you know what I mean. 
20060219, 20:55  #19  
Jun 2005
Near Beetlegeuse
2^{2}×97 Posts 
Quote:
15^2  10^2 = 125 

20060220, 00:55  #20 
Aug 2002
Buenos Aires, Argentina
2^{2}×3×113 Posts 
The trivial cases are:
Odd numbers: Numbers multiple of 4: 
20060220, 04:01  #21  
Bronze Medalist
Jan 2004
Mumbai,India
2052_{10} Posts 
why not?
Quote:
Try working out a 6X6 magic square from 1 to 36. It shoud take you ages but with a method and suitable programming it should be a wheeze I also have logic circuits based on magic squares but Im trying to promote them to INTEL, IBM, etc. first. If they are rejected then I can and am willing to collaborate with you. Mally 

20060220, 20:02  #22 
Aug 2002
Buenos Aires, Argentina
2^{2}×3×113 Posts 
By the way, the differences of two powers not in A074981 are:
Code:
3 ^ 3  5 ^ 2 = 2 13 ^ 3  3 ^ 7 = 10 3 ^ 3  3 ^ 2 = 18 7 ^ 2  3 ^ 3 = 22 3 ^ 3  1 ^ 2 = 26 83 ^ 2  19 ^ 3 = 30 37 ^ 2  11 ^ 3 = 38 17 ^ 2  3 ^ 5 = 46 7 ^ 3  17 ^ 2 = 54 3 ^ 5  13 ^ 2 = 74 11 ^ 2  3 ^ 3 = 94 5 ^ 3  3 ^ 3 = 98 11 ^ 3  35 ^ 2 = 106 3 ^ 5  5 ^ 3 = 118 3 ^ 5  11 ^ 2 = 122 15 ^ 3  57 ^ 2 = 126 173 ^ 2  31 ^ 3 = 138 13 ^ 2  3 ^ 3 = 142 195 ^ 3  2723 ^ 2 = 146 175 ^ 3  2315 ^ 2 = 150 111 ^ 2  23 ^ 3 = 154 3 ^ 5  9 ^ 2 = 162 7 ^ 5  129 ^ 2 = 166 59 ^ 3  453 ^ 2 = 170 7 ^ 3  13 ^ 2 = 174 23 ^ 2  7 ^ 3 = 186 39 ^ 2  11 ^ 3 = 190 3 ^ 5  7 ^ 2 = 194 15 ^ 2  3 ^ 3 = 198 49 ^ 2  3 ^ 7 = 214 3 ^ 5  5 ^ 2 = 218 7 ^ 3  11 ^ 2 = 222 3 ^ 5  3 ^ 2 = 234 3 ^ 5  1 ^ 2 = 242 11 ^ 5  401 ^ 2 = 250 7 ^ 3  9 ^ 2 = 262 39 ^ 3  243 ^ 2 = 270 25 ^ 2  7 ^ 3 = 282 23 ^ 2  3 ^ 5 = 286 7 ^ 3  7 ^ 2 = 294 19 ^ 3  81 ^ 2 = 298 7 ^ 3  5 ^ 2 = 318 7 ^ 3  3 ^ 2 = 334 3 ^ 7  43 ^ 2 = 338 7 ^ 3  1 ^ 2 = 342 61 ^ 2  15 ^ 3 = 346 15 ^ 3  55 ^ 2 = 350 131 ^ 2  7 ^ 5 = 354 27 ^ 3  139 ^ 2 = 362 85 ^ 2  19 ^ 3 = 366 11 ^ 3  31 ^ 2 = 370 25 ^ 2  3 ^ 5 = 382 9 ^ 3  7 ^ 3 = 386 1107 ^ 2  107 ^ 3 = 406 21 ^ 2  3 ^ 3 = 414 