Difference between revisions of "Division Theorem"
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| − | For any positive integers <math> a </math> and <math> b </math>, there exist unique integers <math> q </math> and <math> r </math> such that <math> b = qa + r </math> and <math> 0 \le r < a </math>, with <math> r = 0 </math> if <math> a | b. </math> | + | For any positive integers <math> a </math> and <math> b </math>, there exist unique integers <math> q </math> and <math> r </math> such that <math> b = qa + r </math> and <math> 0 \le r < a </math>, with <math> r = 0 </math> if <math> a | b. </math> We call <math> a </math> the dividend, <math> b </math> the divisor, <math> q </math> the quotient, and <math> r </math> the remainder. |
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[[Category:Mathematics]] | [[Category:Mathematics]] | ||
[[Category:Theorems]] | [[Category:Theorems]] | ||
Latest revision as of 14:37, 1 November 2024
For any positive integers 
and 
, there exist unique integers 
and 
such that 
and 
, with 
if 
We call the dividend, the divisor, the quotient, and the remainder.
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