Difference between revisions of "1993 IMO Problems/Problem 5"
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==Problem== | ==Problem== | ||
| + | Let <math>\mathbb{N} = \{1,2,3, \ldots\}</math>. Determine if there exists a strictly increasing function <math>f: \mathbb{N} \mapsto \mathbb{N}</math> with the following properties: | ||
| + | |||
| + | (i) <math>f(1) = 2</math>; | ||
| + | |||
| + | (ii) <math>f(f(n)) = f(n) + n, (n \in \mathbb{N})</math>. | ||
==Solution== | ==Solution== | ||
| + | Here is my Solution https://artofproblemsolving.com/community/q2h62193p16226748 | ||
| + | |||
| + | Find as ≈ Ftheftics | ||
| + | ==Video solution== | ||
| + | |||
| + | https://youtu.be/IfCBp0608p8 | ||
| + | |||
| + | ==See Also== | ||
| + | |||
| + | {{IMO box|year=1993|num-b=4|num-a=6}} | ||
Latest revision as of 11:30, 21 November 2023
Contents
Problem
Let 
. Determine if there exists a strictly increasing function 
with the following properties:
(i) 
;
(ii) 
.
Solution
Here is my Solution https://artofproblemsolving.com/community/q2h62193p16226748
Find as ≈ Ftheftics
Video solution
See Also
| 1993 IMO (Problems) • Resources | ||
| Preceded by Problem 4 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 6 |
| All IMO Problems and Solutions | ||
