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thehighergeometer.wordpress.com | ||
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mikespivey.wordpress.com
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| | | | | Equations of the form $latex x^3 = y^2 + k$ are called Mordell equations. In this post we're going to prove that the equation $latex x^3 = y^2 -7$ has no integer solutions, using (with one exception) nothing more complicated than congruences. Theorem: There are no integer solutions to the equation $latex x^3 = y^2... | |
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alanrendall.wordpress.com
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| | | | | In a previous post I discussed the Brouwer fixed point theorem and I mentioned the fact that it applies to any non-empty closed bounded convex subset of a Euclidean space, since a subset of this kind is homeomorphic to a closed ball in a Euclidean space. However I did not prove the latter statement. I... | |
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algorithmsoup.wordpress.com
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| | | | | The ``probabilistic method'' is the art of applying probabilistic thinking to non-probabilistic problems. Applications of the probabilistic method often feel like magic. Here is my favorite example: Theorem (Erdös, 1965). Call a set $latex {X}&fg=000000$ sum-free if for all $latex {a, b \in X}&fg=000000$, we have $latex {a + b \not\in X}&fg=000000$. For any finite... | |
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uncommongenders.home.blog
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| | | There is lettragender! -Admin Opal | ||
