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values | messages listlengths 2 20 | used_in listlengths 1 1 | metadata dict | license stringclasses 2
values | tools listlengths 0 0 | url stringlengths 59 129 ⌀ | user_name stringlengths 3 21 ⌀ | user_url stringlengths 42 65 ⌀ |
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\(2, 200, 0, -198\) | Find all integral roots of the equation \( x^2 + px + q = 0 \) given that \( p + q = 198 \). | \(2, 200, 0, -198\) | false | stackflow | [
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all integral roots of the equation \\( x^2 + px + q = 0 \\) given that \\( p + q = 198 \\).",
"reasoning_content": "",
"tool_calls": [],
"tool_call_id": "",
... | [
"nano_v3"
] | {
"reason_low_with_tool": {
"count": 8,
"pass": 5,
"accuracy": 0.625
},
"reason_low_no_tool": {
"count": 8,
"pass": 7,
"accuracy": 0.875
},
"reason_medium_with_tool": {
"count": 8,
"pass": 7,
"accuracy": 0.875
},
"reason_medium_no_tool": {
"count": 8,
"pass": 8,... | cc-by-sa-4.0 | [] | https://math.stackexchange.com/questions/508034/finding-integral-roots-of-x-2-px-q-0-if-p-q-198 | Parth Thakkar | https://math.stackexchange.com/users/70311/parth-thakkar | |
5 | There are $4$ points $A$, $B$, $C$, and $D$ situated in space such that $\angle ABD \cong \angle CBD$. Additionally, $\angle ADB = 2\angle CBD$. Suppose that $AD=4$, $CD=5$, and $AC=9$. Compute the length of $BD$. | 5 | false | aops | [
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nThere are $4$ points $A$, $B$, $C$, and $D$ situated in space such that $\\angle ABD \\cong \\angle CBD$. Additionally, $\\angle ADB = 2\\angle CBD$. Suppose that $AD=4$, $CD=5$... | [
"nano_v3"
] | {
"reason_low_with_tool": {
"count": 8,
"pass": 6,
"accuracy": 0.75
},
"reason_low_no_tool": {
"count": 8,
"pass": 6,
"accuracy": 0.75
},
"reason_medium_with_tool": {
"count": 8,
"pass": 8,
"accuracy": 1
},
"reason_medium_no_tool": {
"count": 8,
"pass": 8,
"... | cc-by-4.0 | [] | null | null | null | |
1 | For a polynomial \( P(x) \) with integer coefficients and integers \( a, b, c \), given the equation
\[ x^{2023} = (x^3 - x - 1)P(x) + ax^2 + bx + c, \]
find the remainder of \( 3b - c \) when divided by 23. | null | true | aops | [
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFor a polynomial \\( P(x) \\) with integer coefficients and integers \\( a, b, c \\), given the equation\n\\[ x^{2023} = (x^3 - x - 1)P(x) + ax^2 + bx + c, \\]\nfind the remaind... | [
"nano_v3"
] | {
"reason_low_with_tool": {
"count": 8,
"pass": 6,
"accuracy": 0.75
},
"reason_low_no_tool": {
"count": 8,
"pass": 1,
"accuracy": 0.125
},
"reason_medium_with_tool": {
"count": 8,
"pass": 8,
"accuracy": 1
},
"reason_medium_no_tool": {
"count": 8,
"pass": 8,
... | cc-by-4.0 | [] | null | null | null | |
\,BE=\frac{1-\sqrt{2}+\sqrt{\,2\sqrt{2}-1\,}}{2}\, | In a unit square ABCD, extend AB as a ray and trace a ray from D that crosses side BC at E and the ray AB at F. Given that EF = 1, what is the length of BE? | null | true | stackflow | [
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn a unit square ABCD, extend AB as a ray and trace a ray from D that crosses side BC at E and the ray AB at F. Given that EF = 1, what is the length of BE?",
"reasoning_con... | [
"nano_v3"
] | {
"reason_low_with_tool": {
"count": 8,
"pass": 7,
"accuracy": 0.875
},
"reason_low_no_tool": {
"count": 8,
"pass": 3,
"accuracy": 0.375
},
"reason_medium_with_tool": {
"count": 8,
"pass": 7,
"accuracy": 0.875
},
"reason_medium_no_tool": {
"count": 8,
"pass": 4,... | cc-by-sa-4.0 | [] | https://math.stackexchange.com/questions/4887956/plane-geometry-unit-square-and-traced-ray-from-vertex | J.P. | https://math.stackexchange.com/users/441771/j-p | |
\text{Center}=0,\qquad\text{Radius of convergence}=1 | Determine the center and radius of convergence of the complex series \(\sum_{n=0}^{\infty} \left(\frac{2-i}{1+5i}\right) z^n\). | Center = 0, Radius = \(\sqrt{\frac{26}{5}}\) | true | stackflow | [
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nDetermine the center and radius of convergence of the complex series \\(\\sum_{n=0}^{\\infty} \\left(\\frac{2-i}{1+5i}\\right) z^n\\).",
"reasoning_content": "",
"tool_c... | [
"nano_v3"
] | {
"reason_low_with_tool": {
"count": 8,
"pass": 2,
"accuracy": 0.25
},
"reason_low_no_tool": {
"count": 8,
"pass": 1,
"accuracy": 0.125
},
"reason_medium_with_tool": {
"count": 8,
"pass": 8,
"accuracy": 1
},
"reason_medium_no_tool": {
"count": 8,
"pass": 8,
... | cc-by-sa-4.0 | [] | https://math.stackexchange.com/questions/3917130/what-is-the-center-and-radius-of-convergence-of-this-complex-series | Jwan622 | https://math.stackexchange.com/users/77211/jwan622 | |
\(\limsup \text{Re } a_n = 1\), \(\liminf \text{Re } a_n = -1\), \(\limsup \text{Im } a_n = 1\), \(\liminf \text{Im } a_n = -1\). | Determine if the real and imaginary parts of the sequence $a_n = i^n$ have a limit superior (lim sup) or limit inferior (lim inf). | \(\limsup \text{Re } a_n = 1\), \(\liminf \text{Re } a_n = -1\), \(\limsup \text{Im } a_n = 1\), \(\liminf \text{Im } a_n = -1\). | false | stackflow | [
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nDetermine if the real and imaginary parts of the sequence $a_n = i^n$ have a limit superior (lim sup) or limit inferior (lim inf).",
"reasoning_content": "",
"tool_calls... | [
"nano_v3"
] | {
"reason_low_with_tool": {
"count": 8,
"pass": 5,
"accuracy": 0.625
},
"reason_low_no_tool": {
"count": 8,
"pass": 6,
"accuracy": 0.75
},
"reason_medium_with_tool": {
"count": 8,
"pass": 7,
"accuracy": 0.875
},
"reason_medium_no_tool": {
"count": 8,
"pass": 5,
... | cc-by-sa-4.0 | [] | https://math.stackexchange.com/questions/1059529/limes-of-a-n-i-n | Falco Winkler | https://math.stackexchange.com/users/186763/falco-winkler | |
\( y'' + 2ay' + a^2y = 0 \) | Find a linear differential equation whose solution is given by \( y = (1 + \frac{ax}{2}) \exp(-ax) \), where \( a \) is a constant. | \( y'' + 2ay' + a^2y = 0 \) | false | stackflow | [
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind a linear differential equation whose solution is given by \\( y = (1 + \\frac{ax}{2}) \\exp(-ax) \\), where \\( a \\) is a constant.",
"reasoning_content": "",
"too... | [
"nano_v3"
] | {
"reason_low_with_tool": {
"count": 8,
"pass": 4,
"accuracy": 0.5
},
"reason_low_no_tool": {
"count": 7,
"pass": 7,
"accuracy": 1
},
"reason_medium_with_tool": {
"count": 8,
"pass": 7,
"accuracy": 0.875
},
"reason_medium_no_tool": {
"count": 8,
"pass": 8,
"... | cc-by-sa-4.0 | [] | https://mathoverflow.net/questions/366581/differential-equation | Jogean Carvalho | https://mathoverflow.net/users/161767/jogean-carvalho | |
601 | "In a \\(25 \\times n\\) grid, each unit square is colored with one of 8 different colors. It is kno(...TRUNCATED) | null | true | aops | [{"role":"user","content":"Solve the following math problem. Make sure to put the answer (and only a(...TRUNCATED) | [
"nano_v3"
] | {"reason_low_with_tool":{"count":8,"pass":3,"accuracy":0.375},"reason_low_no_tool":{"count":8,"pass"(...TRUNCATED) | cc-by-4.0 | [] | null | null | null | |
\displaystyle \frac{27}{5} | "Let \\(a, b > 0\\) with the constraints \\(a + 2b \\leq 5\\) and \\(\\frac{3}{a} + \\frac{4}{b} \\l(...TRUNCATED) | null | true | aops | [{"role":"user","content":"Solve the following math problem. Make sure to put the answer (and only a(...TRUNCATED) | [
"nano_v3"
] | {"reason_low_with_tool":{"count":8,"pass":5,"accuracy":0.625},"reason_low_no_tool":{"count":8,"pass"(...TRUNCATED) | cc-by-4.0 | [] | null | null | null | |
3 | "Determine the list chromatic number $\\chi_l(C_3 \\Box C_5)$ of the graph $C_3 \\Box C_5$. Conjectu(...TRUNCATED) | 3 | false | stackflow | [{"role":"user","content":"Solve the following math problem. Make sure to put the answer (and only a(...TRUNCATED) | [
"nano_v3"
] | {"reason_low_with_tool":{"count":8,"pass":6,"accuracy":0.75},"reason_low_no_tool":{"count":8,"pass":(...TRUNCATED) | cc-by-sa-4.0 | [] | https://mathoverflow.net/questions/335497/the-list-chromatic-number-of-some-special-toroidal-grid-graphs | Jacob.Z.Lee | https://mathoverflow.net/users/42816/jacob-z-lee |
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