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) False: $\displaystyle a = 7\,,\,n=6\,,\,m=3$ Tonio
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.
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 $\displaystyle (m,n)=1 $. See here.
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