Difference between revisions of "1971 IMO Problems/Problem 1"
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+ | ==Problem== | ||
Prove that the following assertion is true for <math>n=3</math> and <math>n=5</math>, and that it is false for every other natural number <math>n>2:</math> | Prove that the following assertion is true for <math>n=3</math> and <math>n=5</math>, and that it is false for every other natural number <math>n>2:</math> | ||
If <math>a_1, a_2,\cdots, a_n</math> are arbitrary real numbers, then <math>(a_1-a_2)(a_1-a_3)\cdots (a_1-a_n)+(a_2-a_1)(a_2-a_3)\cdots (a_2-a_n)+\cdots+(a_n-a_1)(a_n-a_2)\cdots (a_n-a_{n-1})\ge 0.</math> | If <math>a_1, a_2,\cdots, a_n</math> are arbitrary real numbers, then <math>(a_1-a_2)(a_1-a_3)\cdots (a_1-a_n)+(a_2-a_1)(a_2-a_3)\cdots (a_2-a_n)+\cdots+(a_n-a_1)(a_n-a_2)\cdots (a_n-a_{n-1})\ge 0.</math> | ||
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+ | ==Solution== | ||
+ | {{solution}} | ||
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+ | ==See Also== | ||
+ | |||
+ | {{IMO box|year=1963|num-b=First Question|num-a=2}} |
Revision as of 15:01, 17 February 2018
Problem
Prove that the following assertion is true for and , and that it is false for every other natural number
If are arbitrary real numbers, then
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See Also
1963 IMO (Problems) • Resources | ||
Preceded by Problem First Question |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 2 |
All IMO Problems and Solutions |