Michael Lugo
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 Mar 21 comment What is the probability that a point chosen randomly from inside an equilateral triangle is closer to the center than to any of the edges? I like this solution because it makes it clear why the answer is a rational number. From the calculus-based answer this seems a bit mysterious. Mar 16 comment When is $\binom{2n}{n}\cdot \frac{1}{2n}$ an integer? Also see oeis.org/A067348 , which is double this sequence by definition. Mar 11 answered What is the limit of (Odd Numbers Product) / (Even Number Product) Mar 11 revised How to prove that $\forall n \in \Bbb{N}$, $n+\lfloor \sqrt{n} +\frac12 \rfloor$ cannot be a complete square? edited tags Mar 10 comment How to integrate when two functions are being multiplied by each other? You want "integration by parts". Mar 10 comment A five-digit number whose square has its last five digits equal to the number. That's right. I did it for $k = 2$ because doing it for $k = 1$ seemed trivial. Mar 10 answered Log-concave function changes when scalar is added Mar 10 answered A five-digit number whose square has its last five digits equal to the number. Mar 10 answered Factoring Numbers with inner nulls Mar 10 revised Find the moment generating function, mean, and variance of the piecewise function improved formatting Mar 7 comment $N=(x^2-1)(y^2-1)$ has more than one solution oeis.org/A063067 gives a list of such numbers (if you find the first three solutions 360, 504, 2304 by brute force you can find this list). That provides a link to the following notes: mathpages.com/home/kmath275.htm Feb 26 comment How to prove that if $S(n)$ is triangular number for $n \in Z_{+}$, then $a=9$? Perhaps relevant: $S(2)$ is triangular if and only if $a$ is in the sequence at oeis.org/A216134 $(1, 4, 9, 26, 55, \ldots)$. I also find the sporadic solutions $a = 2, 23$ for $n = 3$ and no others for $n \le 5, a \le 10^7$. Feb 25 comment Find two vectors in $P$ and check that their sum is not in $P$. That's right. What's more, that will hold for any plane $P$ that doesn't pass through the origin. Feb 25 answered Find two vectors in $P$ and check that their sum is not in $P$. Feb 24 answered If $X$ is distributed as $U(0,1)$ what is the distribution of $Y = X^3$? Feb 24 comment Solve $\lim_{n\to \infty}\left(\frac{1}{n+1}+\frac{1}{n+2}+\cdots+\frac{1}{n+n}\right)$ without using Riemann sums. How do you get that $\lim_{n \to \infty} H_n - \log n - \gamma = 0$ without using Riemann sums? Feb 23 answered An example that a 2D shape with its centre of mass on its boundary Feb 18 answered What's the chance of drawing 8 or more cards of one suit if you draw 26 cards from a deck? Feb 17 answered Prove the following trigonometric identity without a calculator involved Feb 17 awarded Nice Answer