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...") |
|||
Line 1: | Line 1: | ||
− | + | ==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
Hint
Use the concept of without loss of generality to create an order relation between