metadata
base_model: AI-MO/NuminaMath-7B-TIR
tags:
- alignment-handbook
- generated_from_trainer
- TensorBlock
- GGUF
widget:
- example_title: Math problem
messages:
- role: user
content: >-
For how many values of the constant $k$ will the polynomial
$x^{2}+kx+36$ have two distinct integer roots?
output:
text: >-
### Solution:
1- For the polynomial \\( x^2 + kx + 36 \\) to have two distinct integer
roots, let's denote these roots by \\( r_1 \\) and \\( r_2 \\).
2- According to Vieta's formulas, the sum of the roots \\( r_1 + r_2 \\)
is equal to \\(-k\\), and the product of the roots \\( r_1 \\cdot r_2
\\) is equal to 36.
3- To find the distinct integer pairs \\((r_1, r_2)\\) whose product is
36, we need to determine all pairs of integers \\((r_1, r_2)\\) such
that \\( r_1 \\cdot r_2 = 36 \\) and \\( r_1 \\neq r_2 \\).
4- From the equation \\( r_1 + r_2 = -k \\), for each valid pair
\\((r_1, r_2)\\), we can compute the corresponding value of \\( k \\).
5- Finally, since we need the polynomial to have two distinct integer
roots, we need to ensure that \\( r_1 \\) and \\( r_2 \\) are distinct.
Let's start by finding all pairs \\((r_1, r_2)\\) such that \\( r_1
\\cdot r_2 = 36 \\). We'll then determine the values of \\( k \\) and
ensure the roots are distinct.
```python import itertools
# Find all pairs (r1, r2) such that r1 * r2 = 36 product_36 = 36
factor_pairs = []
for i in range(1, product_36 + 1):
if product_36 % i == 0:
pair = (i, product_36 // i)
if pair[0] != pair[1]: # Ensure distinct pairs
factor_pairs.append(pair)
# Calculate k for each pair and ensure distinct integer roots
valid_k_values = set()
for r1, r2 in factor_pairs:
if r1 != r2:
k = -(r1 + r2)
valid_k_values.add(k)
print((len(valid_k_values), sorted(valid_k_values)))
```
```output
(4, [-37, -20, -15,-13])
```
The distinct integer values of \\( k \\) that make the
polynomial \\( x^2 + kx + 36 \\) have two distinct integer roots are
\\(-37, -20, -15, \\text{and} -13\\).
Therefore, the number of such values of \\( k \\) is:
[ \\boxed{4} \\]
pipeline_tag: text-generation
license: apache-2.0
model-index:
- name: NuminaMath-7B-TIR
results: []
Feedback and support: TensorBlock's Twitter/X, Telegram Group and Discord server
AI-MO/NuminaMath-7B-TIR - GGUF
This repo contains GGUF format model files for AI-MO/NuminaMath-7B-TIR.
The files were quantized using machines provided by TensorBlock, and they are compatible with llama.cpp as of commit b4011.
Prompt template
### Problem: {prompt}
### Solution:
Model file specification
| Filename | Quant type | File Size | Description |
|---|---|---|---|
| NuminaMath-7B-TIR-Q2_K.gguf | Q2_K | 2.532 GB | smallest, significant quality loss - not recommended for most purposes |
| NuminaMath-7B-TIR-Q3_K_S.gguf | Q3_K_S | 2.923 GB | very small, high quality loss |
| NuminaMath-7B-TIR-Q3_K_M.gguf | Q3_K_M | 3.223 GB | very small, high quality loss |
| NuminaMath-7B-TIR-Q3_K_L.gguf | Q3_K_L | 3.489 GB | small, substantial quality loss |
| NuminaMath-7B-TIR-Q4_0.gguf | Q4_0 | 3.725 GB | legacy; small, very high quality loss - prefer using Q3_K_M |
| NuminaMath-7B-TIR-Q4_K_S.gguf | Q4_K_S | 3.749 GB | small, greater quality loss |
| NuminaMath-7B-TIR-Q4_K_M.gguf | Q4_K_M | 3.933 GB | medium, balanced quality - recommended |
| NuminaMath-7B-TIR-Q5_0.gguf | Q5_0 | 4.481 GB | legacy; medium, balanced quality - prefer using Q4_K_M |
| NuminaMath-7B-TIR-Q5_K_S.gguf | Q5_K_S | 4.481 GB | large, low quality loss - recommended |
| NuminaMath-7B-TIR-Q5_K_M.gguf | Q5_K_M | 4.588 GB | large, very low quality loss - recommended |
| NuminaMath-7B-TIR-Q6_K.gguf | Q6_K | 5.284 GB | very large, extremely low quality loss |
| NuminaMath-7B-TIR-Q8_0.gguf | Q8_0 | 6.842 GB | very large, extremely low quality loss - not recommended |
Downloading instruction
Command line
Firstly, install Huggingface Client
pip install -U "huggingface_hub[cli]"
Then, downoad the individual model file the a local directory
huggingface-cli download tensorblock/NuminaMath-7B-TIR-GGUF --include "NuminaMath-7B-TIR-Q2_K.gguf" --local-dir MY_LOCAL_DIR
If you wanna download multiple model files with a pattern (e.g., *Q4_K*gguf), you can try:
huggingface-cli download tensorblock/NuminaMath-7B-TIR-GGUF --local-dir MY_LOCAL_DIR --local-dir-use-symlinks False --include='*Q4_K*gguf'