Difference between revisions of "2005 Austrian Mathematical Olympiad Final Round-Part 1/Problem 5"
(Created page with "5. Find all real solutions (a,b,c,d,e,f) of the system 4a = (b+c+d+e)^4, 4b = (c+d+e+f)^4, ········· 4 f = (a+b+c+d)^4. Try it! Hint: Use the concept of "without los...") |
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| − | + | ==Problem== | |
| − | 4a = (b+c+d+e)^4, | + | Find all real solutions <math>(a,b,c,d,e,f)</math> of the system |
| + | <cmath>4a = (b+c+d+e)^4, | ||
4b = (c+d+e+f)^4, | 4b = (c+d+e+f)^4, | ||
| − | + | \dots | |
| − | 4 f = (a+b+c+d)^4. | + | 4 f = (a+b+c+d)^4.</cmath> |
| − | + | ||
| − | Hint | + | ===Hint=== |
| + | Use the concept of [[without loss of generality]] to create an order relation between <math>a,b,c,d,e,f.</math> | ||
Latest revision as of 15:26, 15 January 2024
Problem
Find all real solutions 
of the system
![\[4a = (b+c+d+e)^4, 4b = (c+d+e+f)^4, \dots 4 f = (a+b+c+d)^4.\]](http://latex.artofproblemsolving.com/e/6/c/e6c98b1510a9de27dcb3545ec84dd7a3c1533d92.png)
Hint
Use the concept of without loss of generality to create an order relation between 
