Victor Miller
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Registered User
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I'm a computational number theorist/discrete mathematician with an interest in arithmetic geometry, data compression and cryptography.
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Apr 26 |
comment |
The Cayley Menger Theorem and integer matrices with row sum 2 @Gunter: not all the coefficients are positive, so that we need to add a sign to $2^k$ -- is it the sign of the permutation? |
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Apr 26 |
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The Cayley Menger Theorem and integer matrices with row sum 2 @Gunter: thank you for a clear a lucid explanation. |
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Apr 26 |
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The Cayley Menger Theorem and integer matrices with row sum 2 @Gunter, I wondered the same. They must mean non-negative. I'll point this out to NJA Sloane. |
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Apr 26 |
revised |
The Cayley Menger Theorem and integer matrices with row sum 2 added reference to paper of Aitken |
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Apr 26 |
asked | The Cayley Menger Theorem and integer matrices with row sum 2 |
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Apr 3 |
comment |
Binary expansion of squares @Mike, You're welcome. I just finished looking at your paper in more detail. Your 3-adic argument for the corresponding base 3 problem is similar to the 2-adic argument that I gave above (though the 2-adic case is a bit simpler since you only have 0/1 coefficients). All I was missing (which is what I alluded to at the end of the paragraph) is the Pade approximation to $\sqrt{1+x}$ that you got from Beukers. |
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Apr 3 |
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Binary expansion of squares @Mike: I can see why you were familiar with Szalay's paper. You were being too modest not mentioning your preprint: math.ubc.ca/~bennett/Be-Selfridge.pdf |
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Apr 3 |
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Binary expansion of squares @Mike: Thanks for the reference. Here's a link to the paper titanic.nyme.hu/~laszalay/publications/TIJNEW.pdf . The heavy lifting was done by Beukers, who showed that there are only at most 4 solutions to $x^2 - D = 2^n$ (variables, $x$ and $n$) |
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Apr 2 |
revised |
Binary expansion of squares separate question from attempts and add sporadic case |
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Apr 2 |
revised |
Binary expansion of squares fixed typos |
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Apr 2 |
revised |
Binary expansion of squares fixed typos, and cleaned up tags |
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Apr 2 |
asked | Binary expansion of squares |
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Mar 9 |
awarded | ● Good Question |
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Dec 23 |
awarded | ● Yearling |
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Nov 24 |
awarded | ● Nice Answer |
