#Brain-Flak, 460 350 270 266 264 188 176 bytes
#Brain-Flak, 460 350 270 266 264 188188 176 bytes
({}[()])(<>((<>()))){{}([(((({}){}))<>)<>({<(({}[()])><>({})<>}>){}<><){}>[)<>[({})]<(())>])](<>)){({}())<>}{}<>{}{}<>(({})){{}{}<>(<(())>)}{}}(<{}{}>)<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<>) The program goes through powers of two and four until it finds one that is larger than the square roota power of two greater than N-1. When it finds it it checks for the divisibility of N-1 by the power of two using modulo and outputs the result
({}[()]) #Subtract one from the input (<>((<>())) ) #Put athree oneones on eachthe other stack { {} #Pop whateverthe crap is onoff the top ([ (( ((({})<(({}) #Multiply by two )<>)<>({<({}[()]>)><>({})<>}{}) #Copy#Multiply andthe Squaretop by four and the powerbottom ofby two <><{}>[<>[({})]<(())>]) #|Check if the square ](<>)){({}())<>}{}<>{}{}<>(({})){{}{}<>(<(())>)}{} #|is#Check if the power of four is greater than N-1 } (<{}{}>) #Remove the power of 4 <>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<{}><>) #Modulo N-1 by the power of two ({}[()])(<>((<>()))){{}([(((({}){}))<>)<>({<(({}[()])><>({})<>}>){}<><){}>[)<>[({})]<(())>])](<>)){({}())<>}{}<>{}{}<>(({})){{}{}<>(<(())>)}{}}(<{}{}>)<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<><{}><>) #Brain-Flak, 460 350 270 266 264 188 bytes
({}[()])(<>(())){{}([(((({}){}))<>)<>({<({}[()])><>({})<>}{}<><{}>[({})]<(())>)](<>)){({}())<>}{}<>{}{}<>(({})){{}{}<>(<(())>)}{}}<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<>) The program goes through powers of two until it finds one that is larger than the square root of N-1. When it finds it it checks for divisibility using modulo and outputs the result
({}[()]) #Subtract one from the input (<>(())) #Put a one on each stack { {} #Pop whatever crap is on the top ([ (( (({}){}) #Multiply by two )<>)<>({<({}[()])><>({})<>}{} #Copy and Square the power of two <><{}>[({})]<(())>) #|Check if the square ](<>)){({}())<>}{}<>{}{}<>(({})){{}{}<>(<(())>)}{} #|is greater than N-1 } <>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<{}><>) #Modulo ({}[()])(<>(())){{}([(((({}){}))<>)<>({<({}[()])><>({})<>}{}<><{}>[({})]<(())>)](<>)){({}())<>}{}<>{}{}<>(({})){{}{}<>(<(())>)}{}}<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<>) #Brain-Flak, 460 350 270 266 264 188 176 bytes
({}[()])(((<>()))){{}([(((({}<(({}){})>){}){})<>[({})(())])](<>)){({}())<>}{}<>{}{}<>(({})){{}{}<>(<(())>)}{}}(<{}{}>)<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<>) The program goes through powers of two and four until it finds a power of two greater than N-1. When it finds it it checks for the divisibility of N-1 by the power of two using modulo and outputs the result
({}[()]) #Subtract one from input (((<>()))) #Put three ones on the other stack { {} #Pop the crap off the top ([( ((({}<(({}){})>){}){}) #Multiply the top by four and the bottom by two <>[({})(())])](<>)){({}())<>}{}<>{}{}<>(({})){{}{}<>(<(())>)}{} #Check if the power of four is greater than N-1 } (<{}{}>) #Remove the power of 4 <>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<{}><>) #Modulo N-1 by the power of two ({}[()])(((<>()))){{}([(((({}<(({}){})>){}){})<>[({})(())])](<>)){({}())<>}{}<>{}{}<>(({})){{}{}<>(<(())>)}{}}(<{}{}>)<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<{}><>) #Brain-Flak, 460 350 270 266 264264 188 bytes
({}[()])((<>(())){{}(<([(({}){})<<>(({})<>)>(<>))>)<>{({}[()])<>(({}()[<>({}<({}[())>)])){{}(<({}({}<><>({}[()])>))>)}{}<>}{}<>{}{}([([<><{}<>]>[({})<]<(())>)](<>)){({}())<>}{}<>{}{}<>(({})){{}(<({}<>(<(())>)}{}({}<>)}{}(<()>)<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<>) ({}[()]) #Subtract one from the input ((<>(())) #Put two ones on the other stack (the top one just has to be#Put a non-zeroone number)on each stack { {} #Pop whatever crap is on the top (<[ (( (({}){}) #Multiply by two <<>(({})<>)>(<>) #Set up to divide #Multiply by N-1two )>) <>{({}[()])<>(({}()[<>({}<({}[())>)])){{}(<({}({}<><>({}[()])>))>)}{}<>}{}<>{}{} #Divide#Copy (Kindof)and Square the power of two ([([ <><{}<>]>[({})<]<(())>) #|Check if the square ](<>)){({}())<>}{}<>{}{}<>(({})){{}(<({}<>(<(())>)}{}({}<>) #Modified#|is lessthangreater checkthan N-1 } {} #Pop the crap (<()>)<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<><{}><>) #Modified Modulo#Modulo ({}[()])((<>(())){{}(<([(({}){})<<>(({})<>)>(<>))>)<>{({}[()])<>(({}()[<>({}<({}[())>)])){{}(<({}({}<><>({}[()])>))>)}{}<>}{}<>{}{}([([<><{}<>]>[({})<]<(())>)](<>)){({}())<>}{}<>{}{}<>(({})){{}(<({}<>(<(())>)}{}({}<>)}{}(<()>)<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<{}><><>) #Brain-Flak, 460 350 270 266 264 bytes
({}[()])((<>())){{}(<((({}){})<<>(({})<>)>(<>))>)<>{({}[()])<>(({}()[({}<({}())>)])){{}(<({}({}<({}[()])>))>)}{}<>}{}<>{}{}([([{}<>]({})<(())>)](<>)){({}())<>}{}<>{}{}<>(({})){{}(<({}<>)>)}{}({}<>)}{}(<()>)<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<>) ({}[()]) #Subtract one from the input ((<>())) #Put two ones on the other stack (the top one just has to be a non-zero number) { {} #Pop whatever crap is on the top (<( (({}){}) #Multiply by two <<>(({})<>)>(<>) #Set up to divide by N-1 )>) <>{({}[()])<>(({}()[({}<({}())>)])){{}(<({}({}<({}[()])>))>)}{}<>}{}<>{}{} #Divide (Kindof) ([([{}<>]({})<(())>)](<>)){({}())<>}{}<>{}{}<>(({})){{}(<({}<>)>)}{}({}<>) #Modified lessthan check } {} #Pop the crap (<()>)<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<>) #Modified Modulo ({}[()])((<>())){{}(<((({}){})<<>(({})<>)>(<>))>)<>{({}[()])<>(({}()[({}<({}())>)])){{}(<({}({}<({}[()])>))>)}{}<>}{}<>{}{}([([{}<>]({})<(())>)](<>)){({}())<>}{}<>{}{}<>(({})){{}(<({}<>)>)}{}({}<>)}{}(<()>)<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<{}><>) #Brain-Flak, 460 350 270 266 264 188 bytes
({}[()])(<>(())){{}([(((({}){}))<>)<>({<({}[()])><>({})<>}{}<><{}>[({})]<(())>)](<>)){({}())<>}{}<>{}{}<>(({})){{}{}<>(<(())>)}{}}<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<>) ({}[()]) #Subtract one from the input (<>(())) #Put a one on each stack { {} #Pop whatever crap is on the top ([ (( (({}){}) #Multiply by two )<>)<>({<({}[()])><>({})<>}{} #Copy and Square the power of two <><{}>[({})]<(())>) #|Check if the square ](<>)){({}())<>}{}<>{}{}<>(({})){{}{}<>(<(())>)}{} #|is greater than N-1 } <>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<{}><>) #Modulo ({}[()])(<>(())){{}([(((({}){}))<>)<>({<({}[()])><>({})<>}{}<><{}>[({})]<(())>)](<>)){({}())<>}{}<>{}{}<>(({})){{}{}<>(<(())>)}{}}<>{({}[()])<>(({}()[({})])){{}(<({}({}))>)}{}<>}{}<>({}<>) Loading
Loading
Loading
Loading
Loading
Loading