When m1 and m2 are coprime their gcd is 1. By convention, a = b (mod 1) is simply understood as the usual equality a = b.
What strikes me as odd is the phrase "is simply understood
as the usual equality a = b"...
if I understand correctly 'a' and 'b' may not be equal!
i.e. 3 = 5 (mod 1) does not mean that 3 = 5.
Am I understanding 'mod' correctly?.
n = 3 (mod 27)
n = 5 (mod 25)
Chinese remainder Theorem states this has a solution iff
3 = 5 (mod 1), since gcd(25,27)=1
a = b (mod 1) should aways be true yes? (since a (mod1) = 0
and b (mod 1) = 0) ?
In this case it would seem Chinese Remainder Theorem is
really only useful if gcd(m1,m2) > 1 otherwise it doesn't
really help you find n1 or n2, (or n).
(The solution for the above is n=30)