ABC Conjecture

Source Notebook

ABC triples by quality

Originator: Bart de Smit

(234 elements)

Examples

Basic Examples

Factorize a triple:

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Check that the ABC conjecture holds for a particular abc triple:

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$Module[{n = 13}, With[{a = ResourceData["ABC Conjecture"][13][[1]], b = ResourceData["ABC Conjecture"][13][[2]]}, Framed[Text[ Style[Column[{Row[{"abc triple: ", a, "+", b, "\[Equal]", Row[(Row[ Apply[Superscript, FactorInteger[#1], {1}] /. Superscript[i_,1] -> i, "\[CenterDot]"] &) /@ {a, b}, "+"], "\[Equal]", a + b, "\[Equal]", Row[Apply[Superscript, FactorInteger[a + b], {1}] /. Superscript[i_,1] -> i, "\[CenterDot]"]}], Row[{"rad[a b c]", " \[Equal] ", "rad"[(a b) (a + b)], " \[Equal] ", "rad"[Row[ Apply[Superscript, FactorInteger[(a b) (a + b)], {1}] /. Superscript[i_,1] -> i, "\[CenterDot]"]], " \[Equal] ", rad[(a b) (a + b)], If[rad[(a b) (a + b)] < a + b, " <", " >"], " c"}], Row[{"rad[a b c]/c", " \[Equal] ", rad[(a b) (a + b)]/(a + b), " == ", N[rad[(a b) (a + b)]]/(a + b), If[N[rad[(a b) (a + b)]]/(a + b) > 1, " > ", " < "], 1}], Row[{"q"[a, b, a + b], " \[Equal] ", N[q[a, b, a + b]], If[q[a, b, a + b] < 1, " <", " >"], 1}]}, Spacings -> 2], 16]]]]]$

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Bibliographic Citation

Enrique Zeleny, "ABC Conjecture" from the Wolfram Data Repository (2021)

Data Resource History

Date Created: 8 September 2021

Source Metadata

Source: http://www.math.leidenuniv.nl/~desmit/abc
Citation: Wikipedia. "abc conjecture." (Sept 26, 2012)., Bart de Smit / ABC triples, 28 September 2012., P. Ball, Proof claimed for deep connection between primes, Nature News, 10 September 2012.

Publisher Information

Prepared for the Wolfram Data Repository By: Enrique Zeleny
Publisher of Record: Enrique Zeleny