How to Solve for Integers Modulo n?

[JJKorman1]

I understand how to solve: a=12mod7 => a = 5, I think, however,
how do you solve for a=7mod12 ?
Stumped

 

[matt grime]

When you say solve, is what you mean is given an integer p find an integer q with 0<=q<n and p==q mod(n) as 7 is between 0 and 11 it solves itself, if you will.

 

[JJKorman1]

Do not understand your response:

if a=12mod7 yields a=5: 5 is the remainder however,
if a=7mod12 what is a? & how do I get there?

Thanks,

JimK

 

[matt grime]

How ling did you spend trying to understand the answer I gave? a=7 is, shall we say, in the reduced form. The remainder after dividing 7 by 12 is 7.

As it stands, when you say solve a=p mod(n) you are not using a well defined phrase. What you might ought to mean is find the remainder on division by n of p, but that isn't immediately obvious from what you wrote. That is, and I realize I'm just restating what I orginally wrote, find the a with 0<=a<n that is the remainder on dividing by n of p. If a is already in that range you are done.

Remember these aren't equals signs, they are equivalences.

 

[Gokul43201]

12 mod 7 == 5 bacause 5 is the difference when you find the largest multiple of 7 that is less than 12 (i.e., 7 itself).

To find what 7 mod 12 is, note that 0 is a multiple of any number. So, now, 0 is the largest multiple of 12 that lies just below 7, and the remainder is 7 itself.

This should be obvious from the reasoning that you are asking what hour 7 refers to on a 12 hr clock.