Difference between revisions of "User:Temperal/The Problem Solver's Resource8"
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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>. | ||
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| + | Guass's Theorem-If <math>a|bc</math> and <math>(a,b) = 1</math>, then <math>a|c</math>. | ||
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[[User:Temperal/The Problem Solver's Resource7|Back to page 7]] | [[User:Temperal/The Problem Solver's Resource9|Continue to page 9]] | [[User:Temperal/The Problem Solver's Resource7|Back to page 7]] | [[User:Temperal/The Problem Solver's Resource9|Continue to page 9]] | ||
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Revision as of 22:05, 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 Guass's Theorem-If
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and 0,1, or 4 
.
, then 
, where 
is the number of relitvely prime numbers lower than 
.
and 
, then 
.
