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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.
Jun
21
revised How prove that:$\varphi(2)+\varphi(3)+\varphi(4)+\cdots+\varphi(n)\ge\frac{n(n-1)}{4}+1$
deleted 2 characters in body
Jun
21
answered How prove that:$\varphi(2)+\varphi(3)+\varphi(4)+\cdots+\varphi(n)\ge\frac{n(n-1)}{4}+1$
Jun
4
comment Can this sum be simplified to closed form?
I'm not sure how to prove it but it seems that the following might be true: set $S(L,b) = \sum_{a=0}^{L-1} \lfloor ab/L\rfloor^2$, and write $L = nb+t$ then $S(L,t) = n(n+1)(2n+1)/6 + S(t,b)$.