Let $\mathbb N$ denote the set of positive integers. A function $f:\mathbb N\to\mathbb N$ is said to be bonza if $f(a)$ divides $b^a-f(b)^{f(a)}$ for all positive integers $a$ and $b$.
Determine the smallest real constant $c$ such that $f(n)\le cn$ for all bonza functions $f$ and all positive integers $n$.
| Agent | Total Messages | Tool Calls | Thinking | Agent Messages |
|---|---|---|---|---|
| b85i | 447 | 216 | 223 | 223 |
| jve2 | 423 | 207 | 211 | 211 |
| wvtn | 463 | 227 | 231 | 231 |
| pj56 | 437 | 214 | 218 | 218 |
| 3gyj | 371 | 181 | 185 | 185 |
| 10ej | 393 | 192 | 196 | 196 |
| Agent | Total Tokens | Input Tokens | Cached Tokens | Thinking Tokens | Output Tokens | Cost |
|---|---|---|---|---|---|---|
| b85i | 15,474,821 | 15,313,786 | 8,780,800 | 82,048 | 161,035 | - |
| jve2 | 14,848,077 | 14,683,194 | 9,242,496 | 77,553 | 164,883 | - |
| wvtn | 15,425,491 | 15,268,795 | 8,800,000 | 83,186 | 156,696 | - |
| pj56 | 16,146,729 | 15,990,158 | 10,318,272 | 78,698 | 156,571 | - |
| 3gyj | 12,532,691 | 12,353,807 | 7,742,336 | 101,536 | 178,884 | - |
| 10ej | 14,402,304 | 14,232,939 | 8,551,488 | 78,435 | 169,365 | - |
| Agent | Total Publications | Published |
|---|---|---|
| b85i | 4 | 0 |
| jve2 | 4 | 3 |
| wvtn | 4 | 1 |
| pj56 | 4 | 4 |
| 3gyj | 8 | 5 |
| 10ej | 5 | 3 |