▁and ▁none ▁of ▁them ▁is ▁repeated : ▁ 4 2 ▁= ▁ 2 ▁× ▁ 3 ▁× ▁ 7 . ▁( If ▁there ▁had ▁been ▁an ▁even '' ▁number ▁of ▁non - re pe ated ▁factors ▁then ▁the ▁sum ▁would ▁have ▁been ▁ 1 ; ▁if ▁there ▁had ▁been ▁any ▁repeated ▁prime ▁factors ▁( e . g ., ▁ 6 0 ▁= ▁ 2 ▁× ▁ 2 ▁× ▁ 3 ▁× ▁ 5 ) ▁then ▁the ▁sum ▁would ▁have ▁been ▁ 0 ; ▁the ▁sum ▁is ▁the ▁M ö b ius ▁function ▁evaluated ▁at ▁ 4 2 .) ▁This ▁hints ▁at ▁the ▁possibility ▁of ▁applying ▁Fourier ▁analysis ▁to ▁number ▁theory . ▁ ▁Sol ving ▁non - tr ig on ometric ▁equations ▁ ▁Vari ous ▁types ▁of ▁equations ▁can ▁be ▁solved ▁using ▁trig on ometry . ▁ ▁For ▁example , ▁a ▁linear ▁difference ▁equation ▁or ▁linear ▁differential ▁equation ▁with ▁constant ▁coefficients ▁has ▁solutions ▁expressed ▁in ▁terms ▁of ▁the ▁eigenvalues ▁of ▁its ▁characteristic ▁equation ; ▁if ▁some ▁of ▁the ▁eigenvalues ▁are ▁complex , ▁the ▁complex ▁terms ▁can ▁be ▁replaced ▁by ▁trig on ometric ▁functions ▁of ▁real ▁terms , ▁showing ▁that ▁the ▁dynamic ▁variable ▁exhib its ▁oscill ations . ▁ ▁Similarly , ▁cub ic ▁equations ▁with ▁three ▁real ▁solutions ▁have ▁an ▁algebraic ▁solution ▁that ▁is ▁un help ful ▁in ▁that ▁it ▁contains ▁cube ▁roots ▁of ▁complex ▁numbers ; ▁again ▁an ▁alternative ▁solution ▁exists ▁in ▁terms ▁of ▁trig on ometric ▁functions ▁of ▁real ▁terms . ▁ ▁References ▁ ▁Category : Tr ig on ometry <0x0A> </s> ▁Test