Difference between revisions of "1981 IMO Problems/Problem 6"
m (→Solution) |
(→Solution) |
||
Line 25: | Line 25: | ||
https://beastacademy.com/ | https://beastacademy.com/ | ||
− | == Solution 2 == | + | == Solution 2 == |
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− |
Revision as of 21:46, 8 April 2024
Problem
The function satisfies
(1)
(2)
(3)
for all non-negative integers . Determine
.
Solution
We observe that and that
, so by induction,
. Similarly,
and
, yielding
.
We continue with ;
;
; and
;
.
It follows that when there are 1984 2s, Q.E.D.
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.
1981 IMO (Problems) • Resources | ||
Preceded by Problem 5 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Last question |
All IMO Problems and Solutions |
https://beastacademy.com/ https://beastacademy.com/