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age 29
visits member for 3 years, 8 months
seen 7 hours ago

Data Scientist @ Explorer Media


May
15
comment Ground plan of Backward direction (<=) - Let $p$ be an odd prime. Prove $x^{2} \equiv -1 \; (mod \, p)$ has a solution $\iff p\equiv 1 \; (mod 4)$
$ \big[ (\frac{p-1}{2})! \big]^2 \equiv -1 (\mod p)$ is a very nice identity, which we prove using various properties of mod $p$ arithmetic. What happens if we use a different starting different combinatorial identity mod $p$ ? Wostonholme's theorem states: $$ \binom{2p}{p} \equiv 2 \mod p^3$$ How do we know the factor's of $p$ cancel out correctly in $\frac{(2p)!}{(p!)^2} $ ?
May
13
revised uniform spanning tree of $2 \times n$ graph
added 91 characters in body
May
13
accepted Looping over $k$-element subsets by switching elements
May
13
revised block matrix multiplication
added 52 characters in body
May
13
revised Probability roots of quadratic lie in unit disc
added 104 characters in body
May
12
revised Probability roots of quadratic lie in unit disc
added a figure to illustrate the coefficients
May
12
revised Probability roots of quadratic lie in unit disc
added a figure to illustrate the coefficients
May
12
answered Probability roots of quadratic lie in unit disc
May
12
comment Primes congruent to 1 mod 6
Indeed $4 > \pi \cdot \tfrac{2}{\sqrt{3}} \approx 3.63$
May
12
revised Dhar's Burning Test - Confusion about Abelian Sandpile Model
more details about sandpile recurrent states
May
12
asked Dhar's Burning Test - Confusion about Abelian Sandpile Model
May
11
revised How often does $p^k$ divide the Fibonacci numbers?
added 226 characters in body
May
11
comment How often does $p^k$ divide the Fibonacci numbers?
@WillJagy So my question is related to the order of the Golden ration $\phi = \frac{1 + \sqrt{5}}{2}$ modulo $p^k$. We know $ (\mathbb{Z}/p\mathbb{Z})^\times$ is cyclic but not the order of any particular element...
May
11
answered $\operatorname{lcm}(n,m,p)\times \gcd(m,n) \times \gcd(n,p) \times \gcd(n,p)= nmp \times \gcd(n,m,p)$, solve for $n,m,p$?
May
11
comment How often does $p^k$ divide the Fibonacci numbers?
@Omnomnomnom How about a quantitative result?
May
11
asked How often does $p^k$ divide the Fibonacci numbers?
May
9
comment Gradient and Swiftest Ascent
This result is not very intuitive, is it?
May
9
comment Product of Elements in SU(2)
$V$ is an arbitrary $2 \times 2$ matrix spanned in the basis of Pauli matrices? Where did you see this formula?
May
9
reviewed Approve suggested edit on Analytical approach to a quadratics problem
May
9
comment Number of Fixed Points in a Map from the Torus to itself using Lefschetz Trace
Here $f$ is my linear map $\left( \begin{array}{cc} 3 & -1 \\ 1 & 3 \end{array}\right)$, $V = \mathbb{R}^2$, $\Gamma = \mathbb{Z}^2$. In this case, $f$ extends to an action on the wedge products $\Lambda^0(\mathbb{R}^2),\Lambda^1(\mathbb{R}^2),\Lambda^2(\mathbb{R}^2)$, globally.