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visits member for 4 years, 1 month
seen 13 hours ago

Mar
31
comment quadratic residues and prime divisor
As far as I know, we don't know if there are infinitely many integers $n$ such that $n^2+1$ prime, it is an open problem.
Mar
27
comment Need suggestions for this real world problem
The kind of problem that you are trying to solve is the Vehicle Routing problem. It's an NP Hard problem which is usually solved using heuristic searches and techniques like constrained integer programming.
Mar
17
comment Properties of a certain integer sequence
Carrying the computation a little further gives the sequence: 1, 1, 2, 2, 3, 5, 6, 8, 11, 17, 25, 33, 41, 52, 80, 139, 204, 245, 289, 410, 692, 1159, 1477, 2010, 2769, 4247, 6128, 7709, 9817
Mar
16
revised Partial fraction decomposition of p'/p
Removed the c
Mar
16
answered Partial fraction decomposition of p'/p
Mar
15
comment Reducing simultaneously a pair of fractions $\frac{a^2}{b},\frac{ a^3}{c}$ using only gcds
You are right, there is no known algorithm even to know if an integer is square-free which does not rely in factorization. Thanks, I hadn't think in your example.
Mar
15
answered Reciprocity problem in I&R “A Classical Introduction in Modern Number Theory”
Mar
14
revised Reducing simultaneously a pair of fractions $\frac{a^2}{b},\frac{ a^3}{c}$ using only gcds
EDIT: Changed to make more clear the question.
Mar
14
comment Reducing simultaneously a pair of fractions $\frac{a^2}{b},\frac{ a^3}{c}$ using only gcds
You would need either to factor $g$ in order to find $d$ or to iterate over the integers up to $\sqrt[6]g$. However I'm changing the question to allow root extraction and avoid iteration. What I'm looking for is a fast way to compute it.
Mar
14
revised Reducing simultaneously a pair of fractions $\frac{a^2}{b},\frac{ a^3}{c}$ using only gcds
Sorry the method I give is not correct
Mar
14
asked Reducing simultaneously a pair of fractions $\frac{a^2}{b},\frac{ a^3}{c}$ using only gcds
Mar
1
comment Closed form for $_2F_1\left(\frac12,\frac23;\,\frac32;\,\frac{8\,\sqrt{11}\,i-5}{27}\right)$
Could you give a reference to understand how the value $g_3 = \eta^6/16$ is found? Thanks.
Feb
13
answered $17$ is a quadratic residue for all primes $p$ such that $p \equiv \pm 3 \mod{8}$?
Dec
22
awarded  Necromancer
Dec
22
revised Generalizing Ramanujan's proof of Bertrand's Postulate: Can Ramanujan's approach be used to show a prime between $4x$ and $5x$ for $x \ge 3$
minor edit
Dec
22
awarded  Revival
Dec
22
answered Generalizing Ramanujan's proof of Bertrand's Postulate: Can Ramanujan's approach be used to show a prime between $4x$ and $5x$ for $x \ge 3$
Dec
18
awarded  Nice Question
Nov
8
awarded  Yearling
Jun
21
revised How prove that:$\varphi(2)+\varphi(3)+\varphi(4)+\cdots+\varphi(n)\ge\frac{n(n-1)}{4}+1$
I have rewritten the proof as the original was very confusing and contained some incorrect statements.