Datasets:
conversations listlengths 2 2 |
|---|
[
{
"from": "human",
"value": "Find all positive integers $n$ such that $n$ divides $2^n - 1$. Prove that your answer is complete."
},
{
"from": "gpt",
"value": "<thinking>\nI need to find all positive integers $n$ such that $n$ divides $2^n - 1$. Prove completeness. We need to solve $n \\mid 2^n ... |
[
{
"from": "human",
"value": "Prove that there are infinitely many primes $p$ such that $p \\equiv 3 \\pmod{4}$."
},
{
"from": "gpt",
"value": "<thinking>\nI need to prove that there are infinitely many primes congruent to 3 modulo 4. This is a classic result in number theory, analogous to Euclid... |
[
{
"from": "human",
"value": "Let $f: \\mathbb{R} \\to \\mathbb{R}$ be a function such that $f(x+y) = f(x) + f(y)$ for all $x, y \\in \\mathbb{R}$. Suppose there exists some interval $[a,b]$ on which $f$ is bounded above. Prove that $f(x) = cx$ for some constant $c \\in \\mathbb{R}$ and all $x \\in \\mathbb{... |
[
{
"from": "human",
"value": "Let $f(x) = \\sum_{n=1}^{\\infty} \\frac{x^n}{n^2}$ for $|x| \\leq 1$. Evaluate $f(x) + f(1-x) + \\ln(x)\\ln(1-x)$ for $0 < x < 1$ and prove your result."
},
{
"from": "gpt",
"value": "<thinking>\nI need to evaluate $f(x) + f(1-x) + \\ln(x)\\ln(1-x)$ for $0 < x < 1$,... |
[
{
"from": "human",
"value": "Let $A$ be an $n \\times n$ real matrix such that $A^3 = A + I$, where $I$ is the identity matrix. Prove that $\\det(A) > 0$."
},
{
"from": "gpt",
"value": "<thinking>\nI need to prove that if $A$ is an $n \\times n$ real matrix such that $A^3 = A + I$, then $\\det(A... |
[
{
"from": "human",
"value": "Let $G$ be a finite group and $H$ a subgroup of index $n$. Prove that there exists a normal subgroup $K$ of $G$ with $K \\subseteq H$ such that $[G:K]$ divides $n!$."
},
{
"from": "gpt",
"value": "<thinking>\nI need to prove the following theorem in group theory:\n\n... |
[
{
"from": "human",
"value": "In a tournament with $2^n$ players, each player has a distinct skill level. In each match, the better player always wins. The tournament is single-elimination with random initial seeding. What is the probability that the second-best player finishes as runner-up? Prove your answe... |
[
{
"from": "human",
"value": "Let $V$ be a finite-dimensional complex vector space and $T: V \\to V$ a linear operator. Prove that $T$ is diagonalizable if and only if for every $T$-invariant subspace $W \\subseteq V$, there exists a $T$-invariant subspace $U \\subseteq V$ such that $V = W \\oplus U$."
},
... |
[{"from":"human","value":"Evaluate $\\int_0^{\\infty} \\frac{\\sin x}{x} dx$ using contour integrati(...TRUNCATED) |
[{"from":"human","value":"Prove that for any prime $p > 3$, the numerator of the reduced fraction fo(...TRUNCATED) |
End of preview. Expand in Data Studio
Kimi K2.6 Thinking 200x — Cleaned
Cleaned version of uniquealexx/Kimi-K2.6-Thinking-200x.
Format — ShareGPT
Each row has a single conversations field in ShareGPT format:
{
"conversations": [
{"from": "human", "value": "Find all positive integers n such that..."},
{"from": "gpt", "value": "<thinking>
I need to find...
</thinking>
The answer is..."}
]
}
Usage with Unsloth
from datasets import load_dataset
dataset = load_dataset("rex099/Kimi-K2.6-Thinking-200x-Cleaned", split="train")
Changes from original
- Removed "The user asks/wants..." openings from all
<thinking>blocks — reasoning traces now read as standalone first-person reasoning - Fixed factual errors in reasoning traces and answers where the final answer contradicted the derivation
- Removed duplicate sentences where the same sentence appeared 3+ times consecutively
- Full reasoning trace length preserved (no trimming)
Stats
| Domain | Count |
|---|---|
| math | 43 |
| analysis | 42 |
| code | 37 |
| science | 31 |
| instruction | 28 |
| logic | 26 |
| Total | 207 |
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