What's with that weird fraction?
Let a 1 , a 2 , a 3 , a 4 be positive real numbers such that
a 1 + a 2 + a 3 + a 4 = 5 2 .
Let the maximum possible value of a 1 a 2 a 3 a 4 be P .
Given that P ≡ n ( m o d 7 ) , find the value of 2 n 3 + n 2 − n + 1 − 1 .
The answer is 0.
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1 solution
Wow......How did you write that AM-GM on the top of that inequality sign?
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\stackrel { } Put anything between the { } signs that you want written above, in this case it is \text{AM-GM}, and right after that (after the } sign) put the inequality, equality, implies, iff, etc. sign you want the text to be above. Maybe an example explains it simpler: what I wrote here was \stackrel { \text{AM-GM} }\le.
Aha!! This is the world's toughest troll!!! :P
Exactly the same as I did. Great solution!
LOL LOL LOL
a 1 a 2 a 3 a 4 ≤ AM-GM ( 4 a 1 + a 2 + a 3 + a 4 ) 4 = ( 4 5 2 ) 4 = 1 3 4 ≡ ( − 1 ) 4 ≡ 1 ≡ n ( m o d 7 ) ⟹ answer = 2 n 3 + n 2 − n + 1 − 1 = 2 1 + 1 − 1 + 1 − 1 = 0 .