Some Number Theory Definitions, Identities and Theorems Skip to main content

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Some Number Theory Definitions, Identities and Theorems

Following are some definitions, identities, and theorems that arise in number theory complete with the link of each proof/explanation.













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Arg(x/y) = Arg(x) - Arg(y)

  It is easy to see that \( \mathrm{arg} \left ( \frac{a}{b} \right ) = \mathrm{arg} \left ( a \right )  - \mathrm{arg} \left ( b \right )  \) for any complex number \( a \) and \( b \). But, this is not the case for the principle value that is \( \mathrm{Arg} \) does not always equal to \( \mathrm{Arg} \left ( a \right ) - \mathrm{Arg} \left ( b \right )  \).
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