Congruence

[kiddopop]

Is the following statement true or false (Explain your answer)?

For all integers a and b and positive integers m, if 2a is congruent to 2b (mod m), then a is congruent to b (mod m).

 

[Deleted member 4993]

Is the following statement true or false (Explain your answer)?

For all integers a and b and positive integers m, if 2a is congruent to 2b (mod m), then a is congruent to b (mod m).

6 ? (14 mod 8)

but

7 ? (7 mod 8)

 

[daon]

In general, one can only cancel "mod m" if the cancellation factor is relatively prime to the modulus.

For example, if 7a = 7b (mod 8) then a=b (mod 8) because gcd(7,8)=1. Such numbers are called primitive roots relative to m (or unit). You'll note that cancellation always holds if the modulus is prime.

 

[Deleted member 4993]

Daon,

Where have you been hiding!!!!

 

[daon]

Ha, not hiding, but i've been keeping myself busy