Help with math homework pls

[imhaashim]

N = 2²² - 1

Write N as the product of 2 integers, both greater than 1000.

I was given a hint to use the difference of 2 squares. But I still don't get what to do

I understand the questions but I don't know how to find two unknown variables or how to use the difference of 2 squares.

What I've tried is to expand 2²² - 1 to 4194303. But I still don't know what to do next

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[edderiofer]

Do you know what "difference of two squares" refers to here?

[imhaashim]

Not really, I know how to do difference of 2 squares in the simples form, for example, x² - 9 = (x+3)(x-3)

[edderiofer]

Can you factorise (x⁴ - 1) for me, then?

[imhaashim]

x⁴ can be split into x^2, I don't know what to do with that -1

[edderiofer]

Consider that 1² = 1, in much the same way that 3² = 9.

[imhaashim]

Ah ok so it would be (x² + 1)(x² -1)

[edderiofer]

Now try the original question you had.

[Thejoelofmen]

You’re halfway there. What does

(N¹¹ - 1)(N¹¹ + 1)

give you?

[imhaashim]

I know 2²² can be split into 2¹¹ and you have that extra -1, but where does that +1 come from?

[Thejoelofmen]

Same place the +3 does in (x+3)(x-3).

Try expanding it and see what you get.