--- 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: \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}\ \ \\\\]" pipeline_tag: text-generation license: apache-2.0 model-index: - name: NuminaMath-7B-TIR results: [] ---

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## AI-MO/NuminaMath-7B-TIR - GGUF This repo contains GGUF format model files for [AI-MO/NuminaMath-7B-TIR](https://huggingface.co/AI-MO/NuminaMath-7B-TIR). The files were quantized using machines provided by [TensorBlock](https://tensorblock.co/), and they are compatible with llama.cpp as of [commit b4011](https://github.com/ggerganov/llama.cpp/commit/a6744e43e80f4be6398fc7733a01642c846dce1d).

Run them on the TensorBlock client using your local machine ↗

## Prompt template ``` ### Problem: {prompt} ### Solution: ``` ## Model file specification | Filename | Quant type | File Size | Description | | -------- | ---------- | --------- | ----------- | | [NuminaMath-7B-TIR-Q2_K.gguf](https://huggingface.co/tensorblock/NuminaMath-7B-TIR-GGUF/blob/main/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](https://huggingface.co/tensorblock/NuminaMath-7B-TIR-GGUF/blob/main/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](https://huggingface.co/tensorblock/NuminaMath-7B-TIR-GGUF/blob/main/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](https://huggingface.co/tensorblock/NuminaMath-7B-TIR-GGUF/blob/main/NuminaMath-7B-TIR-Q3_K_L.gguf) | Q3_K_L | 3.489 GB | small, substantial quality loss | | [NuminaMath-7B-TIR-Q4_0.gguf](https://huggingface.co/tensorblock/NuminaMath-7B-TIR-GGUF/blob/main/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](https://huggingface.co/tensorblock/NuminaMath-7B-TIR-GGUF/blob/main/NuminaMath-7B-TIR-Q4_K_S.gguf) | Q4_K_S | 3.749 GB | small, greater quality loss | | [NuminaMath-7B-TIR-Q4_K_M.gguf](https://huggingface.co/tensorblock/NuminaMath-7B-TIR-GGUF/blob/main/NuminaMath-7B-TIR-Q4_K_M.gguf) | Q4_K_M | 3.933 GB | medium, balanced quality - recommended | | [NuminaMath-7B-TIR-Q5_0.gguf](https://huggingface.co/tensorblock/NuminaMath-7B-TIR-GGUF/blob/main/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](https://huggingface.co/tensorblock/NuminaMath-7B-TIR-GGUF/blob/main/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](https://huggingface.co/tensorblock/NuminaMath-7B-TIR-GGUF/blob/main/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](https://huggingface.co/tensorblock/NuminaMath-7B-TIR-GGUF/blob/main/NuminaMath-7B-TIR-Q6_K.gguf) | Q6_K | 5.284 GB | very large, extremely low quality loss | | [NuminaMath-7B-TIR-Q8_0.gguf](https://huggingface.co/tensorblock/NuminaMath-7B-TIR-GGUF/blob/main/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 ```shell pip install -U "huggingface_hub[cli]" ``` Then, downoad the individual model file the a local directory ```shell 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: ```shell huggingface-cli download tensorblock/NuminaMath-7B-TIR-GGUF --local-dir MY_LOCAL_DIR --local-dir-use-symlinks False --include='*Q4_K*gguf' ```