algebra - Conditions for interchange modulos -


i've been working on problem , hope can me (probably has been studied, don't know). given a , numbers m , n, there special conditions equality

(a (mod m))(mod n)=(a (mod n))(mod m)

to hold? i've been trying come something, until have no clue. can please me this?

thanks!!

yes there is. without loss of generality can assume 'n smaller m' (if same equality holds). hence (a (mod n))(mod m)= (mod n). equality holds iff 'a=n*m*x+y' 'x' , 'y' natural numbers , 'y smaller m' holds, meaning '(int) a/m' multiple of 'n'.


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