If the system of equations \( x=c y+b z, y=a z+c x \) and \( z=b x+...

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If the system of equations \( x=c y+b z, y=a z+c x \) and \( z=b x+a y \) has a non-zero solution and at least one of \( a, b, c \) is a proper fraction, prove that \( a^{3}+b^{3}+c^{3}3 \) and \( a b c-1 \).
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