CMC - Problem 1

Problem 1 (5 points). Let $a,b,c,d$ be complex numbers satisfying

$a+b+c+d=42\text{,}$ $ab+ac+ad+bc+bd+cd=2013\text{, and}$ $a^3+b^3+c^3+d^3+abc+abd+acd+bcd=1337$

Find the last three digits of $a^4+b^4+c^4+d^4+4abcd$ .

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

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