▁closed ▁forms ▁mod ulo ▁exact ▁forms . ▁ ▁Mod ding ▁out ▁In ▁general , ▁mod ding ▁out ▁is ▁a ▁somewhat ▁inform al ▁term ▁that ▁means ▁declaring ▁things ▁equivalent ▁that ▁otherwise ▁would ▁be ▁considered ▁distinct . ▁For ▁example , ▁suppose ▁the ▁sequence   1   4   2   8   5   7 ▁is ▁to ▁be ▁regarded ▁as ▁the ▁same ▁as ▁the ▁sequence   7   1   4   2   8   5 , ▁because ▁each ▁is ▁a ▁cy clic ly - shift ed ▁version ▁of ▁the ▁other : ▁▁ ▁In ▁that ▁case , ▁the ▁phrase ▁" mod ding ▁out ▁by ▁cy clic ▁sh ifts " ▁can ▁also ▁be ▁used . ▁ ▁See ▁also ▁ ▁Ess entially ▁unique ▁List ▁of ▁mathematical ▁j arg on ▁Up ▁to ▁ ▁References ▁ ▁External ▁links ▁ ▁Mod ulo ▁in ▁the ▁J arg on ▁File ▁ ▁Category : Math emat ical ▁termin ology <0x0A> </s> ▁William ▁Cr icht on ▁( 1 5 9 8 – 1 6 9 1 ) ▁was ▁the ▁ 2 nd ▁Earl ▁of ▁Dum f ries . ▁ ▁He ▁object ed ▁to ▁the ▁post hum ous ▁execution ▁of ▁Alexander ▁P eden . ▁ ▁Category : 1 5 9 8 ▁birth s ▁Category : 1 6 9 1 ▁death s ▁Category : E ar ls ▁of ▁Dum f ries ▁Category : 1 7 th - century ▁Scottish ▁pe ers <0x0A> </s> ▁Dr . ▁Sex ▁is ▁a ▁ 1 9 6 4 ▁American ▁film ▁directed ▁by ▁Ted ▁V . ▁Mik els . ▁ ▁The