▁A ▁is ▁the ▁same ▁as ▁B ▁mod ulo ▁C ▁ ▁which ▁means ▁A ▁and ▁B ▁are ▁the ▁same — except ▁for ▁differences ▁account ed ▁for ▁or ▁explained ▁by ▁C . ▁ ▁Us age ▁ ▁Original ▁use ▁ ▁G auss ▁originally ▁intended ▁to ▁use ▁" mod ulo " ▁as ▁follows : ▁given ▁the ▁integers ▁a , ▁b ▁and ▁n , ▁the ▁expression ▁a ▁ ≡ ▁b ▁( mod ▁n ) ▁( pr on ounced ▁" a ▁is ▁con gru ent ▁to ▁b ▁mod ulo ▁n ") ▁means ▁that ▁a   −   b ▁is ▁an ▁integer ▁multiple ▁of ▁n , ▁or ▁equival ently , ▁a ▁and ▁b ▁both ▁leave ▁the ▁same ▁remainder ▁when ▁divided ▁by ▁n . ▁For ▁example : ▁▁ 1 3 ▁is ▁con gru ent ▁to ▁ 6 3 ▁mod ulo ▁ 1 0 ▁ ▁means ▁that ▁▁ 1 3 ▁- ▁ 6 3 ▁is ▁a ▁multiple ▁of ▁ 1 0 ▁( equiv ., ▁ 1 3 ▁and ▁ 6 3 ▁differ ▁by ▁a ▁multiple ▁of ▁ 1 0 ). ▁ ▁Comput ing ▁In ▁computing ▁and ▁computer ▁science , ▁the ▁term ▁can ▁be ▁used ▁in ▁several ▁ways : ▁ ▁In ▁computing , ▁it ▁is ▁typically ▁the ▁mod ulo ▁operation : ▁given ▁two ▁numbers ▁( e ither ▁integer ▁or ▁real ), ▁a ▁and ▁n , ▁a ▁mod ulo ▁n ▁is ▁the ▁remainder ▁of ▁the ▁numerical ▁division ▁of ▁a ▁by ▁n , ▁under ▁certain ▁constraints . ▁ ▁In ▁category ▁theory ▁as ▁applied ▁to ▁functional ▁programming , ▁" oper ating ▁mod ulo " ▁is ▁special