Data update

Task/Modular-arithmetic/00-TASK.txt

@@ -1,10 +1,10 @@
 '''[[wp:Modular arithmetic|Modular arithmetic]]''' is a form of arithmetic (a calculation technique involving the concepts of addition and multiplication) which is done on numbers with a defined [[wp:equivalence relation|equivalence relation]] called ''congruence''.  
 
-For any positive integer <math>p</math> called the ''congruence modulus'', 
-two numbers <math>a</math> and <math>b</math> are said to be ''congruent modulo p'' whenever there exists an integer <math>k</math> such that:
-:<math>a = b + k\,p</math>
+For any positive integer <math>m</math> called the ''congruence modulus'', 
+two numbers <math>a</math> and <math>b</math> are said to be ''congruent modulo m'' whenever there exists an integer <math>k</math> such that:
+:<math>a = b + k\,m</math>
 
-The corresponding set of [[wp:equivalence class|equivalence class]]es forms a [[wp:ring (mathematics)|ring]] denoted <math>\frac{\Z}{p\Z}</math>.  When p is a prime number, this ring becomes a [[wp:field (mathematics)|field]] denoted <math>\mathbb{F}_p</math>, but you won't have to implement the [[wp:multiplicative inverse|multiplicative inverse]] for this task.
+The corresponding set of [[wp:equivalence class|equivalence class]]es forms a [[wp:ring (mathematics)|ring]] denoted <math>\Z/m\Z</math>.  When <math>q=p^k \,(k>0)</math> is a prime power, the ring <math>\Z/q\Z</math> becomes a [[wp:Finite field|finite field]], usually denoted <math>\mathbb{F}_q</math> or <math>\mathrm{GF}(q)</math>, but you won't have to implement the [[wp:multiplicative inverse|multiplicative inverse]] for this task.
 
 Addition and multiplication on this ring have the same algebraic structure as in usual arithmetic, so that a function such as a polynomial expression could receive a ring element as argument and give a consistent result.
 
@@ -22,3 +22,4 @@ In other words, the function is an algebraic expression that could be used with
 ;Related tasks:
 [[Modular exponentiation]]
 <br><br>
+