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finite_geometric_series [2016/06/10 01:42] nikolaj |
finite_geometric_series [2016/06/10 02:00] nikolaj |
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| The proof of the infinitude of primes using Fermat numbers uses this. | The proof of the infinitude of primes using Fermat numbers uses this. | ||
| - | In $\mathbb C$, the equation $(x/b)^n=1$ is solved by $x=b\cdot{\mathrm e}^{2\pi i\frac{k}{n}}$, so | + | In $\mathbb C$, the equation $\left(\frac{x}{b}\right)^n=1$ is solved by $x=b\cdot{\mathrm e}^{2\pi i\frac{k}{n}}$, so |
| $a^n-b^n = (a-b)\prod_{k=1}^{n-1} (a-b\cdot{\mathrm e}^{2\pi i\frac{k}{n}})$ | $a^n-b^n = (a-b)\prod_{k=1}^{n-1} (a-b\cdot{\mathrm e}^{2\pi i\frac{k}{n}})$ | ||
