Question

An integer leaves a remainder 1 when divided by 4. What is the remainder when the square of this integer is divided by 8?

PLSS HELP ASAP

Answer 1

Let's suppose that the integer is x.

We know that x leaves a remainder of 1 when divided by 4, so we can express x as:

x = 4n + 1

where n is some integer.

Now we need to find the remainder when x^2 is divided by 8:

x^2 = (4n + 1)^2

x^2 = 16n^2 + 8n + 1

Notice that the first two terms (16n^2 + 8n) are divisible by 8, so we can ignore them.

The remainder when x^2 is divided by 8 is the same as the remainder of 1 when divided by 8:

x^2 ≡ 1 (mod 8)

Therefore, the remainder when the square of the integer is divided by 8 is 1.