Difference between revisions of "User:Temperal/The Problem Solver's Resource8"
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===Fermat-Euler Identitity=== | ===Fermat-Euler Identitity=== | ||
− | If <math>gcd(a,m)=1</math>, then <math>a^{\phi{m}}\equiv1\pmod{m}</math>, where <math>\phi{m}</math> is the number of | + | If <math>gcd(a,m)=1</math>, then <math>a^{\phi{m}}\equiv1\pmod{m}</math>, where <math>\phi{m}</math> is the number of relatively prime numbers lower than <math>m</math>. |
===Gauss's Theorem=== | ===Gauss's Theorem=== |
Revision as of 09:41, 6 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 Power Mean InequalityFor a real number
Diverging-Converging TheoremA series ErrataAll quadratic residues are |