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bio website tex.stackexchange.com/users/…
location Princeton University
age 24
visits member for 2 years, 9 months
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I am an undergraduate in the Math department at Princeton. For my senior thesis, I am using the memoir class for LaTeX to write a textbook on Real Analysis. Thank you to everyone for all your help!


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awarded  Nice Question
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accepted Proof that $x^2 - 2y^2 = -1$ has a recurring solution for $x$
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comment Proof that $x^2 - 2y^2 = -1$ has a recurring solution for $x$
It seems like the crucial assertion here is that the recurrence relationship exists iff $[\alpha, \beta; \gamma, \delta]^T J [\alpha, \beta; \gamma, \delta] = J$. Why is this true?
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comment System of quadratic Diophantine equations
Do you have links to the results from Matijasevich and Skolem?
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comment Proof that $x^2 - 2y^2 = -1$ has a recurring solution for $x$
I'm looking for a link to a proof that shows that the linear recurrence solution is possible.
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revised Proof that $x^2 - 2y^2 = -1$ has a recurring solution for $x$
added 19 characters in body
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comment Proof that $x^2 - 2y^2 = -1$ has a recurring solution for $x$
Can this be proven without using the $(X, Y)$ formula from the solver? That's really what I'm looking for...
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asked Proof that $x^2 - 2y^2 = -1$ has a recurring solution for $x$
Dec
25
comment Consecutive partitions of positive integers
This paper maths.mq.edu.au/~alf/SomeRecentPapers/183.pdf proves what he refers to as Fermat's four squares theorem. Would you mind explaining how the theorem's statement in terms of arithmetic progressions is equivalent to the $a^2+c^2=2b^2, b^2+d^2=2c^2$ version?
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comment Consecutive partitions of positive integers
Great! This is such a cool result--the fact that we can have consecutive $2$-partitions because the arithmetic progression only has $3$ terms, but that it's impossible for $k>2$. (That trick of using $4(N^2+N)+1=(2N+1)^2$ in the progression is especially clever :))
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awarded  Benefactor
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accepted Consecutive partitions of positive integers