Talk:Waring–Goldbach problem
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Statement wrong?
editThere must be something wrong with the statement of the conjecture because otherwise it is already proven. If we get to choose k we can take k=1 and then we know from partial results on the Goldbach conjecture that every sufficiently large integer can be written as a sum of at most 7 primes. (I think we can take 7 but definitely some finite number.)
I am guessing the problem really asks if for every fixed k we can find t so that every sufficiently large integer is the sum of t k-powers of primes but it might be that something weaker is meant. Clarification would be appreciated. —Preceding unsigned comment added by MathHisSci (talk • contribs) 17:52, June 16, 2010
- I don't see your claimed result (with e.g. 7) listed on Goldbach conjecture#Rigorous results. I'm not familiar enough with these conjectures to answer your question. As you noted, the way it's currently stated, the Waring–Goldbach problem appears to be a much weaker form of the Goldbach conjecture. Justin W Smith talk/stalk 22:15, 16 June 2010 (UTC)
- Every even number can be written as the sum of at most 6 primes according to Wikipedia. Mathworld only states that every even number can be written as the sum of at most 300 000 primes. Either way, since odd numbers are 3 + an even number (expect for a few cases in the beginning that can be checked manually) we find that every number can be written as the sum of at most 300 001 primes according to Mathworld, or 7 according to wiki. (At least if we allow one prime to occur several times.) MathHisSci (talk) 09:46, 22 June 2010 (UTC)
Btw, I don't think it was the QJMath paper that initiated this problem. I think it was his paper, `On the representation of numbers as the sums of the powers of primes', in Math. Z. — Preceding unsigned comment added by 137.222.86.136 (talk) 13:05, 21 December 2015 (UTC)
x-c?
editI found this in this article:
- this is x-c
I changed it to this:
- this is x − c
Am I right that that was what was intended? A minus sign is much longer than a hyphen, and a small space precedes and follows it. I also found such crudities as k=1 instead of k = 1 and fixed them. Michael Hardy (talk) 16:45, 10 November 2023 (UTC)