What is Euclid's lemma?
<!-- Off-topic: See corresponding Wikipedia page for more. --> '''Euclid's lemma''', also called '''Euclid's division lemma''' or '''Euclid's first [[theorem]]''', is an important [[lemma]]. It was made by the [[mathematician]] [[Euclid]]. == Formula ( a = bq +r ) == He basically proposed that for any two [[integers]] (let us call them 'a' and 'b') there exists 2 unique integers (Let us call them ' q ' and ' r ') that satisfies the [[equation]], <big>a = qb + r</big>, where r<a. In the equation, the [[variable]] 'b' is [[Division (mathematics)|dividing]] the variable 'a'. This makes 'b' the [[divisor]] and 'a' as the [[dividend]] 'q' is the [[quotient]] and 'r' is the [[remainder]] The equation thus means that a dividend is [[equal]] to its divisor [[Multiplication|multiplied]] with its quotient and [[Addition|added]] with its remainder. {{math-stub}} [[Category:Number theory]]