Talk:abc conjecture
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[edit]This part
"On April 3, 2020, two Japanese mathematicians announced that Mochizuki's claimed proof would be published in Publications of the Research Institute for Mathematical Sciences (RIMS)"
has to be replaced.
It is now published as a special issue:
https://ems.press/journals/prims/issues/1507 — Preceding unsigned comment added by 158.248.76.166 (talk) 19:19, 14 March 2021 (UTC)
Maniapoto Jackie Newton
[edit]Maniapoto Jackie Newton 122.58.0.183 (talk) 20:16, 2 July 2022 (UTC)
conjectures
[edit]"A number of famous conjectures and theorems in number theory would follow immediately from the abc conjecture or its versions." Is this correct? Will conjectures also follow, or only theorems and proofs of conjectures? 2600:6C67:1C00:5F7E:6DF1:CD52:7E5F:D359 (talk) 15:43, 9 July 2022 (UTC)
A proof of the abc-conjecture would imply the truth of various other well known conjectures. Generisches Maskulinum (talk) 11:31, 1 December 2023 (UTC)
Please add information to the entry
[edit]There are other mathematical theorems related to the subject of value that are not mentioned in the entry. Some of them will be able to be proven if the abc-conjecture will proven. And some with other types of relationships. You can find more topics to put into the entry in the category:abc-conjecture . ינון גלעדי (talk) 22:48, 6 June 2024 (UTC)
Could someone explain the trivial case where a and b are prime?
[edit]"The conjecture essentially states that the product of the distinct prime factors of a b c is usually not much smaller than c "
This is difficult to understand at the moment, because my first instinct was to just try some small numbers, like 5 + 7 = 12. If you pick a and b prime, then coprime is automatic (is this always true?). rad(abc) = 5 * 7 * 2 * 3, which is way bigger than 12. Then you immediately notice, the 2 * 3 isn't needed, the a*b part is already 35 which is way bigger than 12. If a and b are prime, then rad(abc) will be at least (ab) but a + b < ab, so it seems like for any prime a and b, the rad(abc) >> c? So it doesn't at all seem like rad(abc) is usually not much smaller than c.
Where have I gone wrong, what don't I understand? 2A00:23C4:1983:E01:6122:C00D:C83C:5EA0 (talk) 09:21, 6 November 2024 (UTC)