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K $>$ L $>$ M $>$ N are positive integers such that$,$ KM $+$ LN $=$ (K$+$L$-$M$+$N)($-$K$+$L$+$M$+$N)$.$ Prove that KL $+$ MN is not prime.

I'm stumped :/

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    @Chandrasekhar (assuming K+L-M+N, -K+L+M+N > 1)2012-04-15
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    @Chandrasekhar Are you sure, you read the question correctly? Because I don't see how $KL+MN$ is divisible by $K+L-M+N$.2012-04-15
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    @IshaanSingh: Sorry2012-04-15
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    @Ronald $KM + LN$ is divisible by $K+L-M+N$, not $KL+MN$.2012-04-15
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    @IshaanSingh oh! apologies! a nice question, then.2012-04-15
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    Check http://imo.wolfram.com/problemset/IMO2001_solution6.html for solution2012-04-15
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    The second solution in the link KV Raman posted rearranges the condition to $ a^2-ac + c^2 = b^2+bd + d^2$ before proceeding. Those are the norms of $a+c \omega$ and $ b-d\omega$ in the Eisenstein integers $\mathbb{Z}[\omega].$ I wonder if there is an illuminating solution using properties of the Eisenstein integers?2012-04-15

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