Add-ax+ 3by -cz-5by + 9x + 3 cz
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For k = 3 this is already the perfect cube (x2-9x+71) 3. For k = 2, this ... (a-d)2+(b+c)2 = (a+d)2+(b-c)2 ... Proof: ap3+bq3+cr3 = (ax3+by3+cz3)(ax3-by3)3.
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