# Arthur Collé

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bio website facebook.com/arthur.colle location College Park, MD age 22 member for 2 years, 9 months seen yesterday profile views 98

I am an undergraduate student at the University of Maryland, College Park, where I am currently pursuing dual degrees in mathematics and computer science.

I am primarily interested in web application development, real-time data analysis, "software-as-a-service" as a model of software delivery, the impact of macroeconomic fluctuations on foreign exchange markets, and improving the human condition through emerging technological innovations. I like to move fast and break things.

Feel free to contact me by telephone call or text message at (150+151) ((2^5)*(5^2)) (5*3*373). I am always looking for cool open source projects to contribute to so do feel free to contact me if you think my above interests coincide with something special you're working on. Really! Reach out to me! Another option is (my first name)(my last name)@google's-email-service(dawt)com.

# 130 Actions

 Mar5 comment How is 4 a quadratic residue of 7? Right, just realized that any time you get another perfect square as the remainder then the number that yielded that is a quadratic residue Mar5 asked How is 4 a quadratic residue of 7? Feb28 awarded Popular Question Feb27 awarded Nice Question Feb27 comment Show that the gcd of $(n^2, n^2 + n + 1) = 1$ That's what I did but d|n^2 -> d|n is only true for squarefree d, as per Bill Dubuque above. Feb27 comment Show that the gcd of $(n^2, n^2 + n + 1) = 1$ Is there a lemma that if d|a, then d does not divide a+1 ? Feb27 comment Show that the gcd of $(n^2, n^2 + n + 1) = 1$ Is the method of picking some arbitrary d that divides both a good way to proceed however? Feb27 asked Show that the gcd of $(n^2, n^2 + n + 1) = 1$ Feb27 comment How does one show that two general numbers n! + 1 and (n+1)! + 1 are relatively prime? "then d divides n! + 1 and n!" Feb27 accepted How does one show that two general numbers n! + 1 and (n+1)! + 1 are relatively prime? Feb27 comment How does one show that two general numbers n! + 1 and (n+1)! + 1 are relatively prime? André tu m'aides avec mes preuves mathematique depuis trois ans, merci encore une fois! (English: Andre you have assisted me with mathematical proofs for the last three years, thanks again!) Feb27 asked How does one show that two general numbers n! + 1 and (n+1)! + 1 are relatively prime? Feb26 asked Find all integers $n$ (positive, negative, and zero) so that $n^2 + 1$ is divisible by $n + 1$. Dec4 accepted Partial differentiation with respect to multiple variables? Nov29 accepted I don't understand this PDE solution involving Fourier coefficients and orthonormal eigenfunctions. Nov29 comment I don't understand this PDE solution involving Fourier coefficients and orthonormal eigenfunctions. I figured it out, thank you. Nov29 comment I don't understand this PDE solution involving Fourier coefficients and orthonormal eigenfunctions. Nov29 comment I don't understand this PDE solution involving Fourier coefficients and orthonormal eigenfunctions. Okay that makes sense... however I don't see how the statement "if $\lambda < 0$ the condition $X(0) = 0$ tells us that $X(x)$ must be a multiple of $sinh(\sqrt(- \lambda)x)$ because if you have $x = 0$, that only leaves you with $X(0) = \cos(\sqrt(- \lambda) y) + \sin(\sqrt(- \lambda) y)$, something in terms of y. I don't see how this result in terms of y "must be a multiple of" $\sinh(\sqrt(- \lambda) x)$ Nov29 comment I don't understand this PDE solution involving Fourier coefficients and orthonormal eigenfunctions. He also does the same thing on the next page, for $\lambda > 0$, "X must be a multiple of $\sin \sqrt (\lambda \pi)$." Where are these "must be" statements coming from? I just really don't see that hyperbolic one in my above comment. Nov29 comment I don't understand this PDE solution involving Fourier coefficients and orthonormal eigenfunctions. On the bottom of page 64 we test the case of $\lambda < 0$, and he says "the condition X(0) = 0 tells us that X(x) must be a multiple of $\sinh (\sqrt(- \lambda) x)$ ", but previously had defined the general solution of the case where $\lambda < 0$ as $X(x) = \exp{(\pm \sqrt (- \lambda) x)} \cos (\sqrt - \lambda y) + \exp{(\pm \sqrt (- \lambda) x)} \sin (\sqrt - \lambda y)$. When you substitute $x = 0$ into this equation, I believe that $X(0) = cos(\sqrt(- \lambda) y) + sin((\sqrt - \lambda) y)$, which I don't see how is related to $\sinh ((\sqrt - \lambda) x)$ ?