4 ms·
this is for the abc conjecture[1] (I was thinking maybe they were being headline-y about the Riemann hypothesis before I clicked through), which, if proved, wou
by magicalist 14y ago
this is for the abc conjecture[1] (I was thinking maybe they were being headline-y about the Riemann hypothesis before I clicked through), which, if proved, would be extremely interesting due to the number of conjectures and other theorems that have been shown to be equivalent to it or direct consequences of it.
The proof will be well beyond me, but the conjecture itself is pretty accessible, as are many of its connections.
This line from the article was confusing:
> Fifteen and 17 are square free-numbers, but 16 and 18 — being divisible by 42 and 32, respectively — are not.
but that's supposed to be 4^2 and 3^2, respectively.
[1] http://en.wikipedia.org/wiki/Abc_conjecture http://en.wikipedia.org/wiki/Abc_conjecture
- deleted 14y ago[deleted]
- kzahel 14y agoAlso the statement for Fermat's Last Theorem isn't showing the exponents correctly (should be a^n+b^n=c^n)
- alttag 14y agoIt took a moment to puzzle these out (parent and GP's comments). The article would a great deal clearer if the typography made these clearer.
- 3JPLW 14y agoIndeed. Since it's simply copy-pasted from Nature News[0] (with attribution), it may be worthwhile to read it there directly. I didn't understand that the ratio of import was sqp(abc)^r / c until I clicked through to the original story. [0]: http://www.nature.com/news/proof-claimed-for-deep-connection-between-primes-1.11378#b1 http://www.nature.com/news/proof-claimed-for-deep-connection...
- paulrademacher 14y agoAlso: > It states that for integers a+b=c, the ratio of sqp(abc)r/c always has some minimum value greater than zero for any value of r greater than 1. For example, if a=3 and b=125, so that c=128, then sqp(abc)=30 and sqp(abc)2/c = 900/128. In this case, in which r=2, sqp(abc)r/c is nearly always greater than 1, and always greater than zero should be: It states that for integers a+b=c, the ratio of sqp(abc)^r/c always has some minimum value greater than zero for any value of r greater than 1. For example, if a=3 and b=125, so that c=128, then sqp(abc)=30 and sqp(abc)^2/c = 900/128. In this case, in which r=2, sqp(abc)^r/c is nearly always greater than 1, and always greater than zero
- kps 14y agoThe version from Nature does not suffer from this typographical mess. http://www.nature.com/news/proof-claimed-for-deep-connection-between-primes-1.11378 http://www.nature.com/news/proof-claimed-for-deep-connection...