Thread: Need help with 3 homework quesions

Here are my 3 problems:

Prove or disprove that (n^2)-1 is composite whenever n is a positive integer greater than 1

Prove that (a mod m)(b mod m) mod m = ab mod m for all integers a and b whenever m is a positive integer.

Prove or disprove that a mod m + b mod m = (a + b) mod m for all integers a and b whenever m is a positive integer.

Help to Any of these would be appreciated..

thanks

Code:

n^2-1
Composite

Notice that, can be factored, thus it is not prime i.e. composite.
Unless, the factors are trivial, meaning that thus, is the only prime. Thus, is the only prime obtained by this function.

Prove that (a mod m)(b mod m) mod m = ab mod m for all integers a and b whenever m is a positive integer.

Let

,

and:

.

Then:



But

.

Hence:



RonL