本论坛的比较好的内容整理

manthanein

求 <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span tabindex="0" class="MathJax" id="MathJax-Element-3-Frame" role="presentation" style="display: inline-block; position: relative;" data-mathml='<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>a</mi><mn>3</mn></msup><mo>+</mo><msup><mi>b</mi><mn>3</mn></msup><mo>+</mo><msup><mn>1</mn><mn>3</mn></msup><mo>=</mo><msup><mi>c</mi><mn>3</mn></msup></math>'><nobr aria-hidden="true"><span class="math" id="MathJax-Span-20" style="width: 9.12em; display: inline-block;"><span style="width: 1px; height: 0px; overflow: hidden; margin-right: -1px; display: inline-block;"></span><span style="width: 7.35em; height: 0px; font-size: 124%; display: inline-block; position: relative;"><span style="left: 0em; top: -3.98em; position: absolute; clip: rect(2.96em, 1007.35em, 4.21em, -1000em);"><span class="mrow" id="MathJax-Span-21"><span class="msubsup" id="MathJax-Span-22"><span style="width: 1px; height: 0px; overflow: hidden; margin-right: -1px; display: inline-block;"></span><span style="width: 0.95em; height: 0px; display: inline-block; position: relative;"><span style="left: 0em; top: -3.98em; position: absolute; clip: rect(3.39em, 1000.5em, 4.14em, -1000em);"><span class="mi" id="MathJax-Span-23" style="font-family: MathJax_Math-Web; font-style: italic;">a</span>&nbsp;<span style="width: 0px; height: 3.98em; display: inline-block;"></span></span><span style="left: 0.52em; top: -4.34em; position: absolute;"><span class="mn" id="MathJax-Span-24" style="font-family: MathJax_Main-Web; font-size: 70.7%;">3</span>&nbsp;<span style="width: 0px; height: 3.98em; display: inline-block;"></span></span></span></span><span class="mo" id="MathJax-Span-25" style="padding-left: 0.22em; font-family: MathJax_Main-Web;">+</span><span class="msubsup" id="MathJax-Span-26" style="padding-left: 0.22em;"><span style="width: 1px; height: 0px; overflow: hidden; margin-right: -1px; display: inline-block;"></span><span style="width: 0.85em; height: 0px; display: inline-block; position: relative;"><span style="left: 0em; top: -3.98em; position: absolute; clip: rect(3.13em, 1000.42em, 4.14em, -1000em);"><span class="mi" id="MathJax-Span-27" style="font-family: MathJax_Math-Web; font-style: italic;">b</span>&nbsp;<span style="width: 0px; height: 3.98em; display: inline-block;"></span></span><span style="left: 0.42em; top: -4.34em; position: absolute;"><span class="mn" id="MathJax-Span-28" style="font-family: MathJax_Main-Web; font-size: 70.7%;">3</span>&nbsp;<span style="width: 0px; height: 3.98em; display: inline-block;"></span></span></span></span><span class="mo" id="MathJax-Span-29" style="padding-left: 0.22em; font-family: MathJax_Main-Web;">+</span><span class="msubsup" id="MathJax-Span-30" style="padding-left: 0.22em;"><span style="width: 1px; height: 0px; overflow: hidden; margin-right: -1px; display: inline-block;"></span><span style="width: 0.92em; height: 0px; display: inline-block; position: relative;"><span style="left: 0em; top: -3.98em; position: absolute; clip: rect(3.16em, 1000.42em, 4.13em, -1000em);"><span class="mn" id="MathJax-Span-31" style="font-family: MathJax_Main-Web;">1</span>&nbsp;<span style="width: 0px; height: 3.98em; display: inline-block;"></span></span><span style="left: 0.5em; top: -4.37em; position: absolute;"><span class="mn" id="MathJax-Span-32" style="font-family: MathJax_Main-Web; font-size: 70.7%;">3</span>&nbsp;<span style="width: 0px; height: 3.98em; display: inline-block;"></span></span></span></span><span class="mo" id="MathJax-Span-33" style="padding-left: 0.27em; font-family: MathJax_Main-Web;">=</span><span class="msubsup" id="MathJax-Span-34" style="padding-left: 0.27em;"><span style="width: 1px; height: 0px; overflow: hidden; margin-right: -1px; display: inline-block;"></span><span style="width: 0.86em; height: 0px; display: inline-block; position: relative;"><span style="left: 0em; top: -3.98em; position: absolute; clip: rect(3.38em, 1000.42em, 4.14em, -1000em);"><span class="mi" id="MathJax-Span-35" style="font-family: MathJax_Math-Web; font-style: italic;">c</span>&nbsp;<span style="width: 0px; height: 3.98em; display: inline-block;"></span></span><span style="left: 0.43em; top: -4.34em; position: absolute;"><span class="mn" id="MathJax-Span-36" style="font-family: MathJax_Main-Web; font-size: 70.7%;">3</span>&nbsp;<span style="width: 0px; height: 3.98em; display: inline-block;"></span></span></span></span></span>&nbsp;<span style="width: 0px; height: 3.98em; display: inline-block;"></span></span></span><span style="width: 0px; height: 1.29em; overflow: hidden; vertical-align: -0.16em; border-left-color: currentColor; border-left-width: 0px; border-left-style: solid; display: inline-block;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>a</mi><mn>3</mn></msup><mo>+</mo><msup><mi>b</mi><mn>3</mn></msup><mo>+</mo><msup><mn>1</mn><mn>3</mn></msup><mo>=</mo><msup><mi>c</mi><mn>3</mn></msup></math></span></span><script id="MathJax-Element-3" type="math/tex">a^3+b^3+1^3=c^3</script> 的非负整数解,最好有公式
http://bbs.emath.ac.cn/forum.php ... 00&fromuid=9502
(出处: 数学研发论坛)

manthanein

三弦定理与托勒密定理(ptolemy)定理之比较
http://bbs.emath.ac.cn/forum.php ... 05&fromuid=9502
(出处: 数学研发论坛)

manthanein

一道定积分证明题
http://bbs.emath.ac.cn/forum.php ... 75&fromuid=9502
(出处: 数学研发论坛)

manthanein

求 x^2/(( x^2-a)^2 + b^2) 的不定积分
http://bbs.emath.ac.cn/forum.php ... 15&fromuid=9502
(出处: 数学研发论坛)

manthanein

有多少个这样的整数?
http://bbs.emath.ac.cn/forum.php ... 17&fromuid=9502
(出处: 数学研发论坛)

manthanein

求解无穷乘积问题一例
http://bbs.emath.ac.cn/forum.php ... 62&fromuid=9502
(出处: 数学研发论坛)

manthanein

求不定方程<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span tabindex="0" class="MathJax" id="MathJax-Element-3-Frame" role="presentation" style="display: inline-block; position: relative;" data-mathml='<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mi>k</mi><msup><mi>z</mi><mn>2</mn></msup></math>'><nobr aria-hidden="true"><span class="math" id="MathJax-Span-17" style="width: 7.41em; display: inline-block;"><span style="width: 1px; height: 0px; overflow: hidden; margin-right: -1px; display: inline-block;"></span><span style="width: 5.94em; height: 0px; font-size: 124%; display: inline-block; position: relative;"><span style="left: 0em; top: -3.98em; position: absolute; clip: rect(2.99em, 1005.94em, 4.33em, -1000em);"><span class="mrow" id="MathJax-Span-18"><span class="msubsup" id="MathJax-Span-19"><span style="width: 1px; height: 0px; overflow: hidden; margin-right: -1px; display: inline-block;"></span><span style="width: 1em; height: 0px; display: inline-block; position: relative;"><span style="left: 0em; top: -3.98em; position: absolute; clip: rect(3.38em, 1000.52em, 4.14em, -1000em);"><span class="mi" id="MathJax-Span-20" style="font-family: MathJax_Math-Web; font-style: italic;">x</span>&nbsp;<span style="width: 0px; height: 3.98em; display: inline-block;"></span></span><span style="left: 0.57em; top: -4.34em; position: absolute;"><span class="mn" id="MathJax-Span-21" style="font-family: MathJax_Main-Web; font-size: 70.7%;">2</span>&nbsp;<span style="width: 0px; height: 3.98em; display: inline-block;"></span></span></span></span><span class="mo" id="MathJax-Span-22" style="padding-left: 0.22em; font-family: MathJax_Main-Web;">+</span><span class="msubsup" id="MathJax-Span-23" style="padding-left: 0.22em;"><span style="width: 1px; height: 0px; overflow: hidden; margin-right: -1px; display: inline-block;"></span><span style="width: 0.97em; height: 0px; display: inline-block; position: relative;"><span style="left: 0em; top: -3.98em; position: absolute; clip: rect(3.38em, 1000.49em, 4.33em, -1000em);"><span class="mi" id="MathJax-Span-24" style="font-family: MathJax_Math-Web; font-style: italic;">y<span style="width: 0em; height: 1px; overflow: hidden; display: inline-block;"></span></span>&nbsp;<span style="width: 0px; height: 3.98em; display: inline-block;"></span></span><span style="left: 0.54em; top: -4.34em; position: absolute;"><span class="mn" id="MathJax-Span-25" style="font-family: MathJax_Main-Web; font-size: 70.7%;">2</span>&nbsp;<span style="width: 0px; height: 3.98em; display: inline-block;"></span></span></span></span><span class="mo" id="MathJax-Span-26" style="padding-left: 0.27em; font-family: MathJax_Main-Web;">=</span><span class="mi" id="MathJax-Span-27" style="padding-left: 0.27em; font-family: MathJax_Math-Web; font-style: italic;">k</span><span class="msubsup" id="MathJax-Span-28"><span style="width: 1px; height: 0px; overflow: hidden; margin-right: -1px; display: inline-block;"></span><span style="width: 0.94em; height: 0px; display: inline-block; position: relative;"><span style="left: 0em; top: -3.98em; position: absolute; clip: rect(3.38em, 1000.46em, 4.14em, -1000em);"><span class="mi" id="MathJax-Span-29" style="font-family: MathJax_Math-Web; font-style: italic;">z<span style="width: 0em; height: 1px; overflow: hidden; display: inline-block;"></span></span>&nbsp;<span style="width: 0px; height: 3.98em; display: inline-block;"></span></span><span style="left: 0.51em; top: -4.34em; position: absolute;"><span class="mn" id="MathJax-Span-30" style="font-family: MathJax_Main-Web; font-size: 70.7%;">2</span>&nbsp;<span style="width: 0px; height: 3.98em; display: inline-block;"></span></span></span></span></span>&nbsp;<span style="width: 0px; height: 3.98em; display: inline-block;"></span></span></span><span style="width: 0px; height: 1.41em; overflow: hidden; vertical-align: -0.31em; border-left-color: currentColor; border-left-width: 0px; border-left-style: solid; display: inline-block;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mi>k</mi><msup><mi>z</mi><mn>2</mn></msup></math></span></span><script id="MathJax-Element-3" type="math/tex">x^2+y^2=kz^2</script>的通解公式
http://bbs.emath.ac.cn/forum.php ... 26&fromuid=9502
(出处: 数学研发论坛)

manthanein

求数列通项<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span tabindex="0" class="MathJax" id="MathJax-Element-3-Frame" role="presentation" style="display: inline-block; position: relative;" data-mathml='<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><mn>2</mn><msubsup><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><mi>n</mi></mrow><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msubsup><mo>+</mo><mn>1</mn></math>'><nobr aria-hidden="true"><span class="math" id="MathJax-Span-24" style="width: 8.06em; display: inline-block;"><span style="width: 1px; height: 0px; overflow: hidden; margin-right: -1px; display: inline-block;"></span><span style="width: 6.5em; height: 0px; font-size: 124%; display: inline-block; position: relative;"><span style="left: 0em; top: -3.98em; position: absolute; clip: rect(3.01em, 1006.42em, 4.34em, -1000em);"><span class="mrow" id="MathJax-Span-25"><span class="msubsup" id="MathJax-Span-26"><span style="width: 1px; height: 0px; overflow: hidden; margin-right: -1px; display: inline-block;"></span><span style="width: 1.93em; height: 0px; display: inline-block; position: relative;"><span style="left: 0em; top: -3.98em; position: absolute; clip: rect(3.39em, 1000.5em, 4.14em, -1000em);"><span class="mi" id="MathJax-Span-27" style="font-family: MathJax_Math-Web; font-style: italic;">a</span>&nbsp;<span style="width: 0px; height: 3.98em; display: inline-block;"></span></span><span style="left: 0.52em; top: -3.83em; position: absolute;"><span class="texatom" id="MathJax-Span-28"><span class="mrow" id="MathJax-Span-29"><span class="mi" id="MathJax-Span-30" style="font-family: MathJax_Math-Web; font-size: 70.7%; font-style: italic;">n</span><span class="mo" id="MathJax-Span-31" style="font-family: MathJax_Main-Web; font-size: 70.7%;">+</span><span class="mn" id="MathJax-Span-32" style="font-family: MathJax_Main-Web; font-size: 70.7%;">1</span></span></span>&nbsp;<span style="width: 0px; height: 3.98em; display: inline-block;"></span></span></span></span><span class="mo" id="MathJax-Span-33" style="padding-left: 0.27em; font-family: MathJax_Main-Web;">=</span><span class="mn" id="MathJax-Span-34" style="padding-left: 0.27em; font-family: MathJax_Main-Web;">2</span><span class="msubsup" id="MathJax-Span-35"><span style="width: 1px; height: 0px; overflow: hidden; margin-right: -1px; display: inline-block;"></span><span style="width: 1.02em; height: 0px; display: inline-block; position: relative;"><span style="left: 0em; top: -3.98em; position: absolute; clip: rect(3.39em, 1000.5em, 4.14em, -1000em);"><span class="mi" id="MathJax-Span-36" style="font-family: MathJax_Math-Web; font-style: italic;">a</span>&nbsp;<span style="width: 0px; height: 3.98em; display: inline-block;"></span></span><span style="left: 0.52em; top: -4.32em; position: absolute; clip: rect(3.36em, 1000.42em, 4.13em, -1000em);"><span class="texatom" id="MathJax-Span-37"><span class="mrow" id="MathJax-Span-38"><span class="mn" id="MathJax-Span-39" style="font-family: MathJax_Main-Web; font-size: 70.7%;">2</span></span></span>&nbsp;<span style="width: 0px; height: 3.98em; display: inline-block;"></span></span><span style="left: 0.52em; top: -3.83em; position: absolute; clip: rect(3.51em, 1000.49em, 4.14em, -1000em);"><span class="texatom" id="MathJax-Span-40"><span class="mrow" id="MathJax-Span-41"><span class="mi" id="MathJax-Span-42" style="font-family: MathJax_Math-Web; font-size: 70.7%; font-style: italic;">n</span></span></span>&nbsp;<span style="width: 0px; height: 3.98em; display: inline-block;"></span></span></span></span><span class="mo" id="MathJax-Span-43" style="padding-left: 0.22em; font-family: MathJax_Main-Web;">+</span><span class="mn" id="MathJax-Span-44" style="padding-left: 0.22em; font-family: MathJax_Main-Web;">1</span></span>&nbsp;<span style="width: 0px; height: 3.98em; display: inline-block;"></span></span></span><span style="width: 0px; height: 1.39em; overflow: hidden; vertical-align: -0.32em; border-left-color: currentColor; border-left-width: 0px; border-left-style: solid; display: inline-block;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><mn>2</mn><msubsup><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><mi>n</mi></mrow><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msubsup><mo>+</mo><mn>1</mn></math></span></span><script id="MathJax-Element-3" type="math/tex">a_{n+1}=2a_{n}^{2}+1</script>
http://bbs.emath.ac.cn/forum.php ... 94&fromuid=9502
(出处: 数学研发论坛)

manthanein

x^3+y^3=z^3+w^3的一个解
http://bbs.emath.ac.cn/forum.php ... 20&fromuid=9502
(出处: 数学研发论坛)

manthanein

一道积分题
http://bbs.emath.ac.cn/forum.php ... 66&fromuid=9502
(出处: 数学研发论坛)