Difference between revisions of "User:Temperal/The Problem Solver's Resource8"
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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>. | ||
− | ==Errata== | + | ===Errata=== |
All quadratic resiues are 0 or 1<math>\pmod{4}</math>and 0,1, or 4 <math>\pmod{8}</math>. | All quadratic resiues are 0 or 1<math>\pmod{4}</math>and 0,1, or 4 <math>\pmod{8}</math>. | ||
Revision as of 22:09, 5 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
I Chebyshev's InequalityGiven real numbers %{\frac{\sum a_ib_i}{n}} \ge {\frac{\sum a_i}{n}}{\frac{\sum b_i}{n}}%. Minkowsky's InequalityGiven real numbers
Nesbitt's InequalityFor all positive real numbers
Schur's inequalityGiven positive real numbers
Fermat-Euler IdentitityIf Gauss's TheoremIf ErrataAll quadratic resiues are 0 or 1 |