Quantum redactiones paginae "Arithmetica modularis" differant

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Better notation and intro; new section for properties
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* <math display="inline">a \equiv a</math>
* Si <math display="inline">a \equiv b</math>, erit <math display="inline">b \equiv a</math>
* Si <math display="inline">a \equiv b</math> et <math display="inline">b \equiv c</math>, erit <math display="inline">a \equiv c</math>
* Si <math display="inline">a \equiv b</math> et <math display="inline">c \equiv d</math>, erit <math display="inline">a+c \equiv b+d</math>
* Si <math display="inline">a \equiv b</math> et <math display="inline">c \equiv d</math>, erit <math display="inline">ac \equiv bd</math>
* Si <math display="inline">a \equiv b</math>, erit <math display="inline">a^k \equiv b^k</math>(ubi <math display="inline">k \ge 0</math>)
 
At si <math display="inline">ka \equiv kb \pmod{m}</math>, poterunt ''a'' et ''b'' esse incongrui.
 
* Si autem <math display="inline">ka \equiv kb \pmod{m}</math> et ''k'' ad ''m'' est primus, erit <math display="inline">a \equiv b</math>.
 
Si <math display="inline">a \equiv b \pmod{m}</math>, poterunt <math display="inline">c^a</math>et <math display="inline">c^b</math>esse incongrui secundum modulum ''m''.
 
* Si autem <math display="inline">a \equiv b \pmod{\varphi(m)}</math> (ubi φ est [[Euleri functio φ]]) et ''c'' ad ''m'' est primus, erit quidem <math display="inline">c^a \equiv c^b \pmod{m}</math> ([[theorema Euleri]]).
 
== Exemplum ==
Exempli causa, ponamus modulum 6; habemus <math display="inline">5 + 8 \equiv 1 \pmod{6},</math>, quia 5 + 8 = 13, et 13 - 1 per 6 divisibilis est.
 
Secundum modulum 6, numeros hoc modo addimus: