(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I need to prove that any two quadratic integers that are associates must also have the same norm.

2. Relevant equations

If α = a + b√d, the norm of α is N(α) = a^2 - b^2*d.

If two quadratic integers α and β are associates, α divides β, β divides α, and α/β and β/α both equal some unit, although each may be equal to a different unit.

N(unit) = ±1

3. The attempt at a solution

This is what I've done so far:

α/β = ε

N(α/β) = N(ε)

N(α/β) = ±1

N(α)/N(β) = ±1

N(α) = ±N(β)

From here, I guess I need to show that it is impossible to have N(α) = -N(β), but I'm not sure how to do that. Any ideas?

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# Homework Help: Prove that Associates Have the Same Norm

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