Divisor
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Definition
Given two integers, [ilmath]a,b\in\mathbb{Z} [/ilmath], we say that [ilmath]b[/ilmath] divides [ilmath]a[/ilmath], or [ilmath]b[/ilmath] is a divisor of [ilmath]a[/ilmath], or [ilmath]b[/ilmath] is a factor of [ilmath]a[/ilmath][1] if there exists a third integer, [ilmath]c\in\mathbb{Z} [/ilmath] such that:
- [math]a=bc[/math]
Formally, we say:
- Given [ilmath]a,b\in\mathbb{Z} [/ilmath], [ilmath]b[/ilmath] is a divisor of, factor of, or divides [ilmath]a[/ilmath] if [ilmath]\exists c\in\mathbb{Z}[a=bc][/ilmath]
Notes:
- That we may also say [ilmath]a[/ilmath] is a multiple of [ilmath]b[/ilmath]
- The number [ilmath]c[/ilmath] may be called the co-factor of [ilmath]b[/ilmath] in [ilmath]a[/ilmath]
See next
See also
References
- ↑ The mathematics of ciphers, Number theory and RSA cryptography - S. C. Coutinho
