User:Temperal/The Problem Solver's Resource8: Difference between revisions
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==Useful facts and Formulas== | ==Useful facts and Formulas== | ||
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>. | ||
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 relitvely prime numbers lower than <math>m</math>. | 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 relitvely prime numbers lower than <math>m</math>. | ||
Revision as of 21:04, 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. Useful facts and FormulasAll quadratic resiues are 0 or 1 Fermat-Euler Identitity-If |
and 0,1, or 4 
.
, then 
, where 
is the number of relitvely prime numbers lower than 
.
