ise ▁( such ▁as ▁equ ating ▁" mod ulo " ▁with ▁" except ▁for "). ▁For ▁the ▁most ▁part , ▁the ▁term ▁often ▁occurs ▁in ▁statements ▁of ▁the ▁form : ▁ ▁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 . ▁ ▁History ▁Mod ulo ▁is ▁a ▁mathematical ▁j arg on ▁that ▁was ▁introduced ▁into ▁mathematics ▁in ▁the ▁book ▁Dis quisition es ▁Ar ithmet ica e ▁by ▁Carl ▁Friedrich ▁G auss ▁in ▁ 1 8 0 1 . ▁ ▁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 ▁share ▁the ▁same ▁remainder ▁when ▁divided ▁by ▁n . ▁It ▁is ▁the ▁Latin ▁ab l ative ▁of ▁mod ulus , ▁which ▁itself ▁means ▁" a ▁small ▁measure ." ▁▁ ▁The ▁term ▁has ▁gained ▁many ▁mean ings ▁over ▁the ▁years — some ▁exact ▁and ▁some ▁im prec ise . ▁The ▁most ▁general ▁precise ▁definition ▁is ▁simply ▁in ▁terms ▁of ▁an ▁equivalence ▁relation ▁R , ▁where ▁a ▁is ▁equivalent ▁( or ▁con gru ent ) ▁to ▁b ▁mod ulo ▁R ▁if ▁a R b . ▁More ▁inform ally , ▁the ▁term ▁is ▁found ▁in ▁statements ▁of ▁the ▁form :