Fermat–Catalan conjecture
generalization of Fermat's Last Theorem and Catalan's conjecture: a^m+b^n=c^k has only finitely many positive-integer solutions where a, b, c are coprime and m, n, k satisfy 1/m+1/n+1/k<1
| rdfs:label |
"Fermat–Catalan conjecture"@en
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skos:alt |
"Fermat-Catalanova domněnka"@cs
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| schema:description |
"generalization of Fermat's Last Theorem and Catalan's conjecture: a^m+b^n=c^k has only finitely many positive-integer solutions where a, b, c are coprime and m, n, k satisfy 1/m+1/n+1/k<1"@en
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schema:date |
"2026-10-19T20:48:20+00:00"^^xsd:dateTime |
| schema:version | 2558920480 |
| wikibase:identifiers | 3 |
| wikibase:sitelinks | 15 |
| wikibase:statements | 7 |
| p:P138 | wd:statement/Q851604-08f49988-4dff-3ae5-cbbd-9b0ac1af6d22 |
| p:P2534 | wd:statement/Q851604-80c302ac-47c2-5697-5463-9bfdc7bcca48 |
| p:P2812 | wd:statement/Q851604-D991C11E-FE6C-4748-82B9-F1408EBAE6AA |
| p:P31 | wd:statement/Q851604-e6d6ed9d-4e2b-bb85-af7a-7e9c3e2f8307 |
| p:P6104 | wd:statement/Q851604-9F209DB8-9879-44B9-8F8B-0AF8F253981D |
| p:P6366 | wd:statement/Q851604-54B81081-06F4-4293-8470-013C1D4EFD78 |
| p:P646 | wd:statement/Q851604-52987B1A-F526-4CD5-A490-52DBEBC49532 |
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p:direct- |
<https:/ |
| wdt:P138 | Pierre de Fermat |
| wdt:P2534 | "<math class="mwe-math-element mwe-math-element-inline mathjax_ignore" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><mo stretchy="false">(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo stretchy="false">)</mo><mo stretchy="false">∈</mo><mo stretchy="false">(</mo><msup><mrow data-mjx-texclass="ORD"><mi>ℤ</mi></mrow><mrow data-mjx-texclass="ORD"><mo stretchy="false">+</mo></mrow></msup><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mn>6</mn></mrow></msup><mo stretchy="false">|</mo><msup><mi>a</mi><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></msup><mo stretchy="false">+</mo><msup><mi>b</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup><mo stretchy="false">=</mo><msup><mi>c</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msup><mo>,</mo><mspace width="0.278em"></mspace><mn>1</mn><mo lspace="0" rspace="0">/</mo><mi>m</mi><mo stretchy="false">+</mo><mn>1</mn><mo lspace="0" rspace="0">/</mo><mi>n</mi><mo stretchy="false">+</mo><mn>1</mn><mo lspace="0" rspace="0">/</mo><mi>k</mi><mo><</mo><mn>1</mn><mo stretchy="false">=</mo><mo>gcd</mo><mo>⁡</mo><mo stretchy="false">{</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo stretchy="false">}</mo><mo data-mjx-texclass="CLOSE">}</mo></mrow><mo><</mo><mi mathvariant="normal">∞</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P2812 | "Fermat-CatalanConjecture" |
| wdt:P31 | conjecture |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P6366 | "2778195789" |
| wdt:P646 | "/m/05zkdhh" |
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