fundamental theorem of arithmetic
theorem about prime factorization of a number
| rdfs:label |
"fundamental theorem of arithmetic"@en
|
|
skos:alt |
"FTA"@en
"prime factorisation theorem"@en
"prime factorization theorem"@en
"unique factorisation theorem"@en
"unique factorization theorem"@en
"unique-prime-factorization theorem"@en
|
| schema:description |
"theorem about prime factorization of a number"@en
|
|
schema:date |
"2026-10-12T07:40:48+00:00"^^xsd:dateTime |
| schema:version | 2556175397 |
| wikibase:identifiers | 12 |
| wikibase:sitelinks | 70 |
| wikibase:statements | 24 |
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|
p:direct- |
<https:/ |
| wdt:P12800 | "fr:Théorème_fondamental_de_l'arithmétique" |
| wdt:P12888 | "1arith" |
| wdt:P1343 | Mathwords |
| AoPS Wiki | |
| wdt:P1417 | "topic/fundamental-theorem-of-arithmetic" |
| wdt:P1889 | fundamental theorem of algebra |
| wdt:P2534 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mo stretchy="false">(</mo><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">∈</mo><mrow data-mjx-texclass="ORD"><mi>ℤ</mi></mrow><mi mathvariant="normal">∖</mi><mo fence="false" stretchy="false">{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo stretchy="false">−</mo><mn>1</mn><mo fence="false" stretchy="false">}</mo><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mo stretchy="false">(</mo><mi>p</mi><mo stretchy="false">∈</mo><mrow data-mjx-texclass="ORD"><mi>ℙ</mi></mrow><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mo stretchy="false">(</mo><msub><mi>e</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo stretchy="false">≥</mo><mn>1</mn><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">≠</mo><mi>j</mi><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo>⟹</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo stretchy="false">≠</mo><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo>⟹</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mi mathvariant="normal">∃</mi><mo stretchy="false">!</mo><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>,</mo><mo stretchy="false">…</mo><mo>,</mo><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></msub><mo>,</mo><msub><mi>e</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>e</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>,</mo><mo stretchy="false">…</mo><mo>,</mo><msub><mi>e</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></msub><mo stretchy="false">:</mo><mi>a</mi><mo stretchy="false">=</mo><mo stretchy="false">±</mo><msubsup><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow><mrow data-mjx-texclass="ORD"><msub><mi>e</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></msubsup><msubsup><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow><mrow data-mjx-texclass="ORD"><msub><mi>e</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></msubsup><mo stretchy="false">⋯</mo><msubsup><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow><mrow data-mjx-texclass="ORD"><msub><mi>e</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></msub></mrow></msubsup></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P2579 | number theory |
| wdt:P2812 | "FundamentalTheoremofArithmetic" |
| wdt:P31 | theorem |
| wdt:P3417 | "Fundamental-Theorem-of-Arithmetic" |
| wdt:P373 | "Fundamental theorem of arithmetic" |
| wdt:P4215 | "fundamental theorem of arithmetic" |
| wdt:P5008 | Wikipedia:Vital articles/Level/4 |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P6366 | "68625148" |
| wdt:P646 | "/m/0325_" |
| wdt:P6564 | "fundamental-theorem-of-arithmetic" |
| wdt:P6802 |
<http:/ |
| wdt:P7726 | "FundamentalTheoremOfArithmetic" |
| wdt:P8885 | "산술의 기본정리" |
| wdt:P921 | unique factorization domain |
| integer factorization | |
| wdt:P9621 | "teorema-fondamentale-dell-aritmetica" |
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