Talk:Lander, Parkin, and Selfridge conjecture

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Hi, I've created this page; a small lead section has been added. This is quite a technical topic, feel free to suggest how to make it more accessible. Cheers, BRE [forgot to sign originally] Breggen (talk) 01:24, 3 August 2013 (UTC)[reply]

Current status

The sentence It is not known if ... solutions exist that would be counterexamples ... (other than the solutions that follow from the commutative and reflexive properties; there are solution for n = 2, 3, 4). It's not clear what this means exactly? And what is the reference? Spectral sequence (talk) 20:46, 1 August 2013 (UTC)[reply]

This was added by a 3rd party, I can elaborate. I think in my version I simply had "non-trivial". Breggen (talk) 01:23, 3 August 2013 (UTC)[reply]

The passage other than the solutions that follow from the commutative and reflexive properties was added by Georgia Guy on 23 July. I reverted it today (albeit a tad belatedly), and he put it back in again. Georgia Guy, I ask again that you please remember not to put original research into Wikipedia articles. Also, please remember WP:BRD -- Bold (which you were when you put it in), Revert (which I just did), and then Discuss, which you should do next here on the talk page rather than undoing a reversion.

Perhaps you could give an example of a solution that follows from the commutative and reflexive properties, requiring the caveat.

I'm taking it out again, as per WP:BRD and because there is a consensus in this section of the talk page that the passage is incomprehensible and unreferenced. Duoduoduo (talk) 16:18, 16 August 2013 (UTC)[reply]

Commutative property: 2^5 + 3^5 = 3^5 + 2^5 (a+b = b+a)

Reflexive property: 2^5 + 3^5 = 2^5 + 3^5 (a = a)

Georgia guy (talk) 16:20, 16 August 2013 (UTC)[reply]

These are not counterexamples to the conjecture, which is that

if

\sum _{i=1}^{n}a_{i}^{k}=\sum _{j=1}^{m}b_{j}^{k}

, where a_i ≠ b_j are positive integers for all 1 ≤ i ≤ n and 1 ≤ j ≤ m, then m+n ≥ k

since they violate a_i ≠ b_j. Duoduoduo (talk) 16:59, 16 August 2013 (UTC)[reply]

An similar conjecture

Conjecture: if ±(a_1)^n±(a_2)^n±(a_3)^n±...±(a_m)^n=0 (all a_i are positive integers) and m > 2, then n ≤ 2^m-2. Is it right? That is, if $\sum _{i=1}^{n}a_{i}^{k}=\sum _{j=1}^{m}b_{j}^{k}$ , where a_i ≠ b_j are positive integers for all 1 ≤ i ≤ n and 1 ≤ j ≤ m, then 2^m+n-2 ≥ k. — Preceding unsigned comment added by 49.214.6.73 (talk) 08:43, 16 April 2015 (UTC)[reply]