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Show that N(a+bi) = even => a+bi divisible by 1+i

So, N(a+bi) = a^{2}+b^{2}= even

so 2 divides a^{2}+b^{2}

Write 2 = (1+i)(1-i)

so we have 1+i divides a^{2}+b^{2}

so 1+i divides either (a+bi) or (a-bi)

if 1+i divides a+bi we are done

what if 1+i divides a-bi though?

Thats where I'm stuck!

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# Homework Help: Gaussian integers and norms

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