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---
base_model: AI-MO/NuminaMath-7B-TIR
license: apache-2.0
pipeline_tag: text-generation
tags:
- alignment-handbook
- generated_from_trainer
- llama-cpp
- gguf-my-repo
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: \n1- For the polynomial \\\\( x^2 + kx + 36 \\\\) to have\
\ two distinct integer roots, let's denote these roots by \\\\( r_1 \\\\) and\
\ \\\\( r_2 \\\\).\n\n\n2- 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.\n\n\n3- 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 \\\\).\n\n\n4- From the equation \\\\\
( r_1 + r_2 = -k \\\\), for each valid pair \\\\((r_1, r_2)\\\\), we can compute\
\ the corresponding value of \\\\( k \\\\).\n\n\n5- Finally, since we need the\
\ polynomial to have two distinct integer roots, we need to ensure that \\\\\
( r_1 \\\\) and \\\\( r_2 \\\\) are distinct.\nLet'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.\n\
```python import itertools\n# Find all pairs (r1, r2) such that r1 * r2 = 36\
\ product_36 = 36 factor_pairs = []\nfor i in range(1, product_36 + 1):\n if\
\ product_36 % i == 0:\n pair = (i, product_36 // i)\n if pair[0] != pair[1]:\
\ # Ensure distinct pairs\n factor_pairs.append(pair)\n \n # Calculate\
\ k for each pair and ensure distinct integer roots\n valid_k_values = set()\n\
\ for r1, r2 in factor_pairs:\n if r1 != r2:\n k = -(r1 + r2)\n\
\ valid_k_values.add(k)\n \n print((len(valid_k_values), sorted(valid_k_values)))\n\
\ ```\n \n ```output\n (4, [-37, -20, -15,-13])\n ```\n The distinct integer\
\ values of \\\\( k \\\\) that make the\npolynomial \\\\( x^2 + kx + 36 \\\\\
) have two distinct integer roots are \\\\(-37, -20, -15, \\\\text{and} -13\\\
\\).\nTherefore, the number of such values of \\\\( k \\\\) is:\n[ \\\\boxed{4}\
\ \\\\]"
model-index:
- name: NuminaMath-7B-TIR
results: []
---
# martintmv/NuminaMath-7B-TIR-Q4_K_M-GGUF
This model was converted to GGUF format from [`AI-MO/NuminaMath-7B-TIR`](https://huggingface.co/AI-MO/NuminaMath-7B-TIR) using llama.cpp via the ggml.ai's [GGUF-my-repo](https://huggingface.co/spaces/ggml-org/gguf-my-repo) space.
Refer to the [original model card](https://huggingface.co/AI-MO/NuminaMath-7B-TIR) for more details on the model.
## Use with llama.cpp
Install llama.cpp through brew (works on Mac and Linux)
```bash
brew install llama.cpp
```
Invoke the llama.cpp server or the CLI.
### CLI:
```bash
llama-cli --hf-repo martintmv/NuminaMath-7B-TIR-Q4_K_M-GGUF --hf-file numinamath-7b-tir-q4_k_m.gguf -p "The meaning to life and the universe is"
```
### Server:
```bash
llama-server --hf-repo martintmv/NuminaMath-7B-TIR-Q4_K_M-GGUF --hf-file numinamath-7b-tir-q4_k_m.gguf -c 2048
```
Note: You can also use this checkpoint directly through the [usage steps](https://github.com/ggerganov/llama.cpp?tab=readme-ov-file#usage) listed in the Llama.cpp repo as well.
Step 1: Clone llama.cpp from GitHub.
```
git clone https://github.com/ggerganov/llama.cpp
```
Step 2: Move into the llama.cpp folder and build it with `LLAMA_CURL=1` flag along with other hardware-specific flags (for ex: LLAMA_CUDA=1 for Nvidia GPUs on Linux).
```
cd llama.cpp && LLAMA_CURL=1 make
```
Step 3: Run inference through the main binary.
```
./llama-cli --hf-repo martintmv/NuminaMath-7B-TIR-Q4_K_M-GGUF --hf-file numinamath-7b-tir-q4_k_m.gguf -p "The meaning to life and the universe is"
```
or
```
./llama-server --hf-repo martintmv/NuminaMath-7B-TIR-Q4_K_M-GGUF --hf-file numinamath-7b-tir-q4_k_m.gguf -c 2048
```
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