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messages list |
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[
{
"role": "system",
"content": "You are a helpful, expert AI tutor. Solve the problem by breaking it down step-by-step."
},
{
"role": "user",
"content": "Given the following problem:\n\nLet $f$ be a function taking the integers to the integers such that\n\\[f(m + n) + f(mn - 1) = f(m) f(n) + 2\\... |
[
{
"role": "system",
"content": "You are a helpful, expert AI tutor. Solve the problem by breaking it down step-by-step."
},
{
"role": "user",
"content": "Let $T$ be the set of complex numbers of the form $x + yi,$ where $x$ and $y$ are real numbers, such that\n\\[\\frac{1}{2} \\le x \\le \\frac{... |
[
{
"role": "system",
"content": "You are a helpful, expert AI tutor. Solve the problem by breaking it down step-by-step."
},
{
"role": "user",
"content": "Vova has recently learned what a circulaton in a graph is. Recall the definition: let G = (V, E) be a directed graph. A circulation f is such ... |
[{"role":"system","content":"You are a helpful, expert AI tutor. Solve the problem by breaking it do(...TRUNCATED) |
[{"role":"system","content":"You are a helpful, expert AI tutor. Solve the problem by breaking it do(...TRUNCATED) |
[{"role":"system","content":"You are a helpful, expert AI tutor. Solve the problem by breaking it do(...TRUNCATED) |
[{"role":"system","content":"You are a helpful, expert AI tutor. Solve the problem by breaking it do(...TRUNCATED) |
[{"role":"system","content":"You are a helpful, expert AI tutor. Solve the problem by breaking it do(...TRUNCATED) |
[{"role":"system","content":"You are a helpful, expert AI tutor. Solve the problem by breaking it do(...TRUNCATED) |
[{"role":"system","content":"You are a helpful, expert AI tutor. Solve the problem by breaking it do(...TRUNCATED) |
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