## Prove how and why the square root of

Prove how and why the square root of 2 can NOT be written as a rational number.

## Show that the square root of

Show that the square root of a prime number is not rational.

## What is the result of 0.1/0.01 +

What is the result of 0.1/0.01 + 0.01/0.001 + 0.001/0.0001=?

## What is the result of

What is the result of ((-1/2)^-3)^2?

## The natural number 28A9B consists of different numbers and

The natural number 28A9B consists of different numbers and A is not equal to 0. When the number is divided by 9 the remainder is 7 and when it is divided by 5, the remainder is 1. What is A-B=?

## What is the ones digit of

What is the ones digit of the number (23)^23?

## What is (6^6)+(6^5) in

What is (6^6)+(6^5) in (mod5)?

## Prove: There are infinitely many prime numbers p of the form 4n+3.

Prove: There are infinitely many prime numbers p of the form 4n+3. In other words, show that there exist infinitely many positive integers, n, such that the number 4n+1 is prime.

## (a) Let G = GL(2,R) be the general linear group. Let H=GL(2,Q) and

(a) Let G = GL(2,R) be the general linear group. Let H=GL(2,Q) and K= SL(2,R) = {A is an element of G: det (A) =1} Show that H,K are subgroups of G (b) Let p be a prime number and a is an element of Z. Prove that a^p ,is equivalent to, a mod p

## Simplify: (a/(a-b))+(b/a^2+ab+b^2))

Simplify: (a/(a-b))+(b/a^2+ab+b^2))- (2/(a^3-b^3)