Difference between revisions of "User:Temperal/The Problem Solver's Resource8"
(→General Mean Inequality: inequality) |
(I think the Power mean inequality is the same thing as the general mean inequality (at least, their descriptions here are)) |
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===Gauss's Theorem=== | ===Gauss's Theorem=== | ||
If <math>a|bc</math> and <math>(a,b) = 1</math>, then <math>a|c</math>. | If <math>a|bc</math> and <math>(a,b) = 1</math>, then <math>a|c</math>. | ||
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===Diverging-Converging Theorem=== | ===Diverging-Converging Theorem=== |
Revision as of 17:40, 9 October 2007
Intermediate Number TheoryThese are more complex number theory theorems that may turn up on the USAMO or Pre-Olympiad tests. This will also cover diverging and converging series, and other such calculus-related topics. General Mean InequalityTake a set of functions Note that
, if Chebyshev's InequalityGiven real numbers
Minkowsky's InequalityGiven real numbers
Nesbitt's InequalityFor all positive real numbers
Schur's inequalityGiven positive real numbers
Fermat-Euler IdentitityIf Gauss's TheoremIf Diverging-Converging TheoremA series ErrataAll quadratic residues are |