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Find the sum of all positive integral a<2014a<2014a<2014 such that ax4+1ax^4+1ax4+1 can be factored to (bx2−cx+1)(bx2+cx+1)(bx^2-cx+1)(bx^2+cx+1)(bx2−cx+1)(bx2+cx+1) for all xxx where b,cb,cb,c are integers.
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