https://artofproblemsolving.com/wiki/index.php?title=Chittur_Gopalakrishnavishwanathasrinivasaiyer_Lemma&feed=atom&action=historyChittur Gopalakrishnavishwanathasrinivasaiyer Lemma - Revision history2024-03-28T19:21:29ZRevision history for this page on the wikiMediaWiki 1.31.1https://artofproblemsolving.com/wiki/index.php?title=Chittur_Gopalakrishnavishwanathasrinivasaiyer_Lemma&diff=162526&oldid=prevMathsweat notreally at 00:59, 21 September 20212021-09-21T00:59:10Z<p></p>
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<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>  We know that an <math>x</math> exists that equal to <math>42\, \cdot</math> <math>\text{mod} \sqrt{4761}.</math> This <math>x</math> is very powerful in competition math problems. Usually coming up on JMO and AMO geo problems. The Euler Line intersects the radical axis at <math>(x^n, n^x)</math> where <math>n</math> is the number of composite factors the radius has. This theorem is also used in Newton's Sums, as the <math>n</math>th root unity is the same thing as <math>x^n</math> <math>\text{mod}</math> <math>(42*10\cdot(70-1)^n).</math> Finally, you'll se it in combo! The number ways you can shuffle <math>n</math> things into <math>n^2 + nk + 1</math> items where <math>k</math> is the number of partitions in an item is the <math>x^{23\cdot3}.</math> My <del class="diffchange diffchange-inline">coach </del>Iyer Sir approved this nice lemma.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>  We know that an <math>x</math> exists that equal to <math>42\, \cdot</math> <math>\text{mod} \sqrt{4761}.</math> This <math>x</math> is very powerful in competition math problems. Usually coming up on JMO and AMO geo problems. The Euler Line intersects the radical axis at <math>(x^n, n^x)</math> where <math>n</math> is the number of composite factors the radius has. This theorem is also used in Newton's Sums, as the <math>n</math>th root unity is the same thing as <math>x^n</math> <math>\text{mod}</math> <math>(42*10\cdot(70-1)^n).</math> Finally, you'll se it in combo! The number ways you can shuffle <math>n</math> things into <math>n^2 + nk + 1</math> items where <math>k</math> is the number of partitions in an item is the <math>x^{23\cdot3}.</math> My <ins class="diffchange diffchange-inline">coaches </ins>Iyer Sir <ins class="diffchange diffchange-inline">and Barnes </ins>approved this nice lemma.</div></td></tr>
</table>Mathsweat notreallyhttps://artofproblemsolving.com/wiki/index.php?title=Chittur_Gopalakrishnavishwanathasrinivasaiyer_Lemma&diff=153019&oldid=prevReadyplayerone at 01:29, 1 May 20212021-05-01T01:29:55Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 01:29, 1 May 2021</td>
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<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>  We know that an <math>x</math> exists that equal to <math>\text{<del class="diffchange diffchange-inline">42*10 </del>mod <del class="diffchange diffchange-inline">(</del>\sqrt{4761}.</math> This <math>x</math> is very powerful in competition math problems. Usually coming up on JMO and AMO geo problems. The Euler Line intersects the radical axis at <math>(x^n, n^x)</math> where <math>n</math> is the number of composite factors the radius has. This theorem is also used in Newton's Sums, as the <math>n</math>th root unity is the same thing as <math>x^n</math> <math>\text{mod}</math> <math>(42*10\cdot(70-1)^n).</math> Finally, you'll se it in combo! The number ways you can shuffle <math>n</math> things into <math>n^2 + nk + 1</math> items where <math>k</math> is the number of partitions in an item is the <math>x^{23\cdot3}.</math> My coach Iyer Sir approved this nice lemma.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>  We know that an <math>x</math> exists that equal to <ins class="diffchange diffchange-inline"><math>42\, \cdot</math> </ins><math>\text{mod<ins class="diffchange diffchange-inline">} </ins>\sqrt{4761}.</math> This <math>x</math> is very powerful in competition math problems. Usually coming up on JMO and AMO geo problems. The Euler Line intersects the radical axis at <math>(x^n, n^x)</math> where <math>n</math> is the number of composite factors the radius has. This theorem is also used in Newton's Sums, as the <math>n</math>th root unity is the same thing as <math>x^n</math> <math>\text{mod}</math> <math>(42*10\cdot(70-1)^n).</math> Finally, you'll se it in combo! The number ways you can shuffle <math>n</math> things into <math>n^2 + nk + 1</math> items where <math>k</math> is the number of partitions in an item is the <math>x^{23\cdot3}.</math> My coach Iyer Sir approved this nice lemma.</div></td></tr>
</table>Readyplayeronehttps://artofproblemsolving.com/wiki/index.php?title=Chittur_Gopalakrishnavishwanathasrinivasaiyer_Lemma&diff=153018&oldid=prevReadyplayerone at 01:28, 1 May 20212021-05-01T01:28:15Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 01:28, 1 May 2021</td>
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<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>  We know that an <math>x</math> exists that equal to <math>\text{<del class="diffchange diffchange-inline">420 </del>mod <del class="diffchange diffchange-inline">69</del>}.</math> This <math>x</math> is very powerful in competition math problems. Usually coming up on JMO and AMO geo problems. The Euler Line intersects the radical axis at <math>(x^n, n^x)</math> where <math>n</math> is the number of composite factors the radius has. This theorem is also used in Newton's Sums, as the <math>n</math>th root unity is the same thing as <math>x^n</math> <math>\text{mod}</math> <math>(<del class="diffchange diffchange-inline">420</del>\<del class="diffchange diffchange-inline">cdot69</del>^n).</math> Finally, you'll se it in combo! The number ways you can shuffle <math>n</math> things into <math>n^2 + nk + 1</math> items where <math>k</math> is the number of partitions in an item is the <math>x^{<del class="diffchange diffchange-inline">69</del>}.</math> My coach Iyer Sir approved this nice lemma.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>  We know that an <math>x</math> exists that equal to <math>\text{<ins class="diffchange diffchange-inline">42*10 </ins>mod <ins class="diffchange diffchange-inline">(\sqrt{4761</ins>}.</math> This <math>x</math> is very powerful in competition math problems. Usually coming up on JMO and AMO geo problems. The Euler Line intersects the radical axis at <math>(x^n, n^x)</math> where <math>n</math> is the number of composite factors the radius has. This theorem is also used in Newton's Sums, as the <math>n</math>th root unity is the same thing as <math>x^n</math> <math>\text{mod}</math> <math>(<ins class="diffchange diffchange-inline">42*10</ins>\<ins class="diffchange diffchange-inline">cdot(70-1)</ins>^n).</math> Finally, you'll se it in combo! The number ways you can shuffle <math>n</math> things into <math>n^2 + nk + 1</math> items where <math>k</math> is the number of partitions in an item is the <math>x^{<ins class="diffchange diffchange-inline">23\cdot3</ins>}.</math> My coach Iyer Sir approved this nice lemma.</div></td></tr>
</table>Readyplayeronehttps://artofproblemsolving.com/wiki/index.php?title=Chittur_Gopalakrishnavishwanathasrinivasaiyer_Lemma&diff=153017&oldid=prevReadyplayerone: Created page with " We know that an <math>x</math> exists that equal to <math>\text{420 mod 69}.</math> This <math>x</math> is very powerful in competition math problems. Usually coming up on JM..."2021-05-01T01:26:56Z<p>Created page with " We know that an <math>x</math> exists that equal to <math>\text{420 mod 69}.</math> This <math>x</math> is very powerful in competition math problems. Usually coming up on JM..."</p>
<p><b>New page</b></p><div> We know that an <math>x</math> exists that equal to <math>\text{420 mod 69}.</math> This <math>x</math> is very powerful in competition math problems. Usually coming up on JMO and AMO geo problems. The Euler Line intersects the radical axis at <math>(x^n, n^x)</math> where <math>n</math> is the number of composite factors the radius has. This theorem is also used in Newton's Sums, as the <math>n</math>th root unity is the same thing as <math>x^n</math> <math>\text{mod}</math> <math>(420\cdot69^n).</math> Finally, you'll se it in combo! The number ways you can shuffle <math>n</math> things into <math>n^2 + nk + 1</math> items where <math>k</math> is the number of partitions in an item is the <math>x^{69}.</math> My coach Iyer Sir approved this nice lemma.</div>Readyplayerone