Consider congruences (http://planetmath.org/Congruences) of the form
where the coefficients and are rational integers. Solving the congruence means finding all the integer values of which satisfy (1).
since one would otherwise have and the first term could be left out of (1). Now, we say that the degree of the congruence (1) is .
If is a solution of (1) and , then by the properties of congruences (http://planetmath.org/Congruences),
and thus also is a solution. Therefore, one regards as different roots of a congruence modulo only such values of which are incongruent modulo .
One can think that the congruence (1) has as many roots as is found in a complete residue system modulo .
|Date of creation||2013-03-22 18:52:23|
|Last modified on||2013-03-22 18:52:23|
|Last modified by||pahio (2872)|
|Defines||degree of congruence|
|Defines||root of congruence|