Difference between revisions of "2025 IMO Problems/Problem 3"
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Let <math>\mathbb{N}</math> denote the set of positive integers. A function <math>f: \mathbb{N} \rightarrow \mathbb{N}</math> is said to be bonza if <math>f(a)</math> divides <math>b^{a} - f(b)^{f(a)}</math> for all positive integers <math>a</math> and <math>b</math>. Determine the smallest real constant <math>c</math> such that <math>f(n) \leq cn</math> for all bonza functions <math>f</math> and all positive integers <math>n</math>. | Let <math>\mathbb{N}</math> denote the set of positive integers. A function <math>f: \mathbb{N} \rightarrow \mathbb{N}</math> is said to be bonza if <math>f(a)</math> divides <math>b^{a} - f(b)^{f(a)}</math> for all positive integers <math>a</math> and <math>b</math>. Determine the smallest real constant <math>c</math> such that <math>f(n) \leq cn</math> for all bonza functions <math>f</math> and all positive integers <math>n</math>. | ||
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| + | ==Video solution== | ||
| + | https://www.youtube.com/watch?v=vPqUTG4CW8w | ||
Revision as of 21:57, 15 July 2025
Let 
denote the set of positive integers. A function 
is said to be bonza if 
divides 
for all positive integers 
and 
. Determine the smallest real constant 
such that 
for all bonza functions 
and all positive integers 
.
