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)

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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)

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

Tonio

Quote:

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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)

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Of course tonio is right; and fyi if we change mn to lcm(m,n) then it becomes true.

Quote:

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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)

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This is true iff $\displaystyle (m,n)=1 $.

See here.