modular aritmetic?

Question

hi

i'm tryna work out how to do modular arithmetic, lets say I have

a = 0.5 mod(5)

how can I calculate what a is?

thx

Answer 1

There are infinitely many possible values for a. a = 0.5 mod(5) means that a - 0.5 is evenly divisible by 5, or equivalently that when a is divided by 5, the remainder is 0.5. That is to say, a = 5k + 0.5, where k is any integer. Some examples of possible values for a are 0.5, 5.5, 100.5, 120015.5, -4.5, and -24.5. Note that the negative numbers are 0.5 greater than a negative integer multiply of 5, not 0.5 less. If the entire problem is as given, then a = 5k + 0.5, k in Z (by which I mean "k is in the set of all integers"), is a complete and correct answer. If you have some other information, there may be a different, single or more restricted answer.

Answer 2

It's rather unusual to have fractions in a modular arithmetic equation. Do you mean 2 a = 1 mod 5 ?

If yes, multiply both sides by 3, you get 6 a = 3 mod 5.
Since 6 = 1 mod 5, you find a = 3 mod 5.

Any integer of the form 3 + 5 k (k integer) does the job.