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User:Temperal/The Problem Solver's Resource8

< User:Temperal
Revision as of 21:05, 5 October 2007 by Xpmath (talk | contribs) (→‎Useful facts and Formulas)



The Problem Solver's Resource
Introduction | Other Tips and Tricks | Methods of Proof | You are currently viewing page 8.

Intermediate Number Theory

These 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 Formulas

All quadratic resiues are 0 or 1$\pmod{4}$and 0,1, or 4 $\pmod{8}$.

Fermat-Euler Identitity-If $gcd(a,m)=1$, then $a^{\phi{m}}\equiv1\pmod{m}$, where $\phi{m}$ is the number of relitvely prime numbers lower than $m$.

Gauss's Theorem-If $a|bc$ and $(a,b) = 1$, then $a|c$.


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