Answer to Question #5300 in Combinatorics | Number Theory for Niren gupta

Question

prove the relation a=L(mod m) is aequivalent relation?

Answer 1

to prove we must
show that this relation is reflexive, symmetric and transitive
reflexive:
a=a( mod m) it is obvious statement by the definition of mod m
symmetric if
a=b(mod m) then b=a (mod m) to prove this we can write if a=b(mod m) then a have
the same remainder after division by m as b. so b have the same remainder after
division by m as a so b=a(mod m)
transitive: if a=b(mod m) and b=c(mod m)
then a=c(mod m) . if a=b (mod m) so a have reminder after division by m and its
equal to the same remainder of b , from b=c(mod m) we have that b have reminder
after division by m and its equal to the same remainder of c. so a and c have
the same remainder . so a=c(mod m)