Math Help - Congruence

1. Congruence

For all integers a and positive integers m and n, if a is congruent to 1 (mod m) and a is congruent to 1 (mod n), then a is congruent to 1 (mod mn)

2. Originally Posted by leilani13
For all integers a and positive integers m and n, if a is congruent to 1 (mod m) and a is congruent to 1 (mod n), then a is congruent to 1 (mod mn)

False: $a = 7\,,\,n=6\,,\,m=3$

Tonio

3. Originally Posted by leilani13
For all integers a and positive integers m and n, if a is congruent to 1 (mod m) and a is congruent to 1 (mod n), then a is congruent to 1 (mod mn)
Of course tonio is right; and fyi if we change mn to lcm(m,n) then it becomes true.

4. Originally Posted by leilani13
For all integers a and positive integers m and n, if a is congruent to 1 (mod m) and a is congruent to 1 (mod n), then a is congruent to 1 (mod mn)
This is true iff $(m,n)=1$.

See here.