[ \frac1a^2 + a + 1 = \fraca-1a^3 - 1 \quad \text(since a^3 - 1 = (a-1)(a^2+a+1)\text). ]
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The Internet Archive is a treasure trove of out-of-print Soviet-era math books. [ \frac1a^2 + a + 1 = \fraca-1a^3
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