Matches in Wikidata for { <http://www.wikidata.org/entity/Q180345> ?p ?o ?g. }
- Q180345 prefLabel "有理數根定理" @default.
- Q180345 prefLabel "有理根定理" @default.
- Q180345 prefLabel "유리근 정리" @default.
- Q180345 P1417 Q180345-B7306C49-5E4F-48F8-9F07-C3C0098ABBF9 @default.
- Q180345 P2534 Q180345-0AC6FD4C-5BF3-4B94-9BB8-2DD16D4B8CDB @default.
- Q180345 P2812 Q180345-0E47CB1C-AE4E-4229-8182-6DFCFEA30BD2 @default.
- Q180345 P31 Q180345-0C8BEB3C-9128-4451-94F3-B6334D8DCD40 @default.
- Q180345 P31 Q180345-1A2C6887-D23B-4024-9544-E8EA6C8F4B45 @default.
- Q180345 P6104 Q180345-A49E43B6-CF20-40A9-84F5-066D8D4B68AB @default.
- Q180345 P6366 Q180345-4DDD9EC9-57D7-4F7C-956D-B3A6BB45C119 @default.
- Q180345 P646 Q180345-B8ADB318-58F0-4557-824B-EF0D1BE54AB8 @default.
- Q180345 P6366 27166021 @default.
- Q180345 P1417 "topic/rational-root-theorem" @default.
- Q180345 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \forall x\in \mathbb {Q} \forall a_{0},a_{n}\in \mathbb {Z} \setminus \{0\}\forall a_{1},\dotsc ,a_{n-1}\in \mathbb {Z} \colon a_{n}x^{n}+a_{n-1}x^{n-1}+\dotsb +a_{0}=0\implies \exists p,q\in \mathbb {Z} \colon (x=p/q\land \gcd\{p,q\}=1\land p\mid a_{0}\land q\mid a_{n})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀<!-- ∀ --></mi> <mi>x</mi> <mo>∈<!-- ∈ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Q</mi> </mrow> <mi mathvariant="normal">∀<!-- ∀ --></mi> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>∈<!-- ∈ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mo class="MJX-variant">∖<!-- ∖ --></mo> <mo fence="false" stretchy="false">{</mo> <mn>0</mn> <mo fence="false" stretchy="false">}</mo> <mi mathvariant="normal">∀<!-- ∀ --></mi> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>…<!-- … --></mo> <mo>,</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> <mo>∈<!-- ∈ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mo>:<!-- : --></mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>+</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <mo>⋯<!-- ⋯ --></mo> <mo>+</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mspace width="thickmathspace" /> <mo stretchy="false">⟹<!-- ⟹ --></mo> <mspace width="thickmathspace" /> <mi mathvariant="normal">∃<!-- ∃ --></mi> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo>∈<!-- ∈ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mo>:<!-- : --></mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>=</mo> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>q</mi> <mo>∧<!-- ∧ --></mo> <mo movablelimits="true" form="prefix">gcd</mo> <mo fence="false" stretchy="false">{</mo> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo fence="false" stretchy="false">}</mo> <mo>=</mo> <mn>1</mn> <mo>∧<!-- ∧ --></mo> <mi>p</mi> <mo>∣<!-- ∣ --></mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>∧<!-- ∧ --></mo> <mi>q</mi> <mo>∣<!-- ∣ --></mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall x\in \mathbb {Q} \forall a_{0},a_{n}\in \mathbb {Z} \setminus \{0\}\forall a_{1},\dotsc ,a_{n-1}\in \mathbb {Z} \colon a_{n}x^{n}+a_{n-1}x^{n-1}+\dotsb +a_{0}=0\implies \exists p,q\in \mathbb {Z} \colon (x=p/q\land \gcd\{p,q\}=1\land p\mid a_{0}\land q\mid a_{n})}</annotation> </semantics> </math>" @default.
- Q180345 P2812 "RationalZeroTheorem" @default.
- Q180345 P31 Q1085860 @default.
- Q180345 P31 Q65943 @default.
- Q180345 P6104 Q8487137 @default.
- Q180345 P6366 "27166021" @default.
- Q180345 P646 "/m/06l4l" @default.