Tito Piezas III

2,640 reputation

523

bio	website	sites.google.com/site/tpiezas/…
	location	Canada
	age
visits	member for	2 years, 5 months
	seen	29 mins ago
stats	profile views	572

There is a also Wordpress.com blog that supplements my "Collection of Algebraic Identities" website. The blog is about mathematical stuff that I find interesting.

	2,640 reputation	bio	website	sites.google.com/site/tpiezas/…	visits	member for	2 years, 5 months
523 badges		location	Canada		seen	29 mins ago

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47 Questions

views newest activity votes

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answers

kviews

How did Hermite calculate $e^{\pi\sqrt{163}}$ in 1859?

real-analysis math-history

jan 26 '12 at 3:52 J. M. 38.9k

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answer

493

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A new continued fraction for Apéry's constant, $\zeta(3)$?

nov 25 at 12:24 J. M. 38.9k

votes

answers

974

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Why do some Fibonacci numbers appear in an approximation for $e^{\pi\sqrt{163}}$?

number-theory sequences-and-series fibonacci-numbers

apr 26 '12 at 15:44 Alex 92

votes

answers

kviews

Does the equation $x^4+y^4+1 = z^2$ have a non-trivial solution?

abstract-algebra number-theory diophantine-equations

dec 4 '11 at 10:03 t.b. 43.1k

votes

answer

228

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The Fibonacci sum $\sum_{n=0}^\infty \frac{1}{F_{2^n}}$ generalized

real-analysis sequences-and-series limit fibonacci-numbers

jan 25 at 3:07 Tito Piezas III 2,640

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answers

230

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How did Letac solve $x_1^k + x_2^k + \dots +x_9^k = 0$ for $k = 1, 3, 5, 7$ in 1942?

elementary-number-theory reference-request diophantine-equations

may 17 at 20:49 Tito Piezas III 2,640

votes

answers

466

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Prove the Fibonacci sum $\sum \limits_{n=0}^{\infty}\frac{F_n}{p^n} = \frac{p}{p^2-p-1}$

sequences-and-series fibonacci-numbers

nov 25 at 12:07 J. M. 38.9k

votes

answer

215

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What is the binomial sum $\sum_{n=1}^\infty \frac{1}{n^5\,\binom {2n}n}$ in terms of zeta functions?

special-functions binomial-coefficients analytic-number-theory riemann-zeta zeta-functions

may 14 '12 at 18:32 Tito Piezas III 2,640

votes

answer

242

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Why do the Fibonacci numbers recycle these formulas?

number-theory sequences-and-series recurrence-relations fibonacci-numbers

jul 9 at 9:33 J. M. 38.9k

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answer

208

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On the zeta sum $\sum_{n=1}^\infty[\zeta(5n)-1]$ and others

complex-analysis special-functions riemann-zeta gamma-function

jun 11 '12 at 23:37 Zander 3,842

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answers

147

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On Ramanujan's Question 359

trigonometry

feb 21 at 9:59 Tito Piezas III 2,640

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answers

200

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The Fermat prime 257 and binomial sum $\sum_{n=0}^\infty \frac{(-1)^n}{\binom {8n}{4n}}$?

prime-numbers binomial-coefficients logarithms

jun 4 '12 at 21:53 Robert Israel 86.3k

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answer

217

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A new formula for Apery's constant and other zeta(s)?

sequences-and-series riemann-zeta

jul 30 at 13:43 J. M. 38.9k

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answer

256

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On the Diophantine equation $a^2+b^2 = c^2+k$

number-theory limit diophantine-equations

jul 7 at 13:09 mercio 11.2k

votes

answer

178

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Proving a series for the Watson Triple Integrals?

sequences-and-series integral pi

nov 26 '11 at 0:37 J. M. 38.9k

votes

answers

286

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The radical solution of a solvable 17th degree equation

number-theory abstract-algebra polynomials galois-theory

sep 20 '11 at 14:28 Tito Piezas III 2,640

votes

answers

245

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An infinite product for $\left(\frac{\eta(13\tau)}{\eta(\tau)}\right)^2$? (revised)

special-functions modular-forms

jul 5 at 17:49 Tito Piezas III 2,640

votes

answer

109

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Sum of n squares $(x_1^2+x_2^2 + \dots + x_n^2)^2 (y_1^2+y_2^2 + \dots + y_n^2) = z_1^2+z_2^2 + \dots + z_n^2$

linear-algebra abstract-algebra

jan 30 '12 at 21:52 Davide Giraudo 56.2k

votes

answer

125

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Finding x in $\frac{\,_2F_1(\frac{1}{5},\frac{4}{5},\,1,\,1-x)}{\,_2F_1(\frac{1}{5},\frac{4}{5},\,1,\,x)} = \sqrt{n}$

special-functions elliptic-functions hypergeometric-function

jan 3 at 18:37 Tito Piezas III 2,640

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answer

111

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On the Dirichlet beta function sum $\sum_{k=2}^\infty\Big[1-\beta(k) \Big]$

special-functions zeta-functions

jun 24 '12 at 17:11 Eric 33.2k

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answers

158

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What does Pfister's 8-Square Identity look like?

abstract-algebra

jan 31 '12 at 1:20 Robert Israel 86.3k

votes

answer

363

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A Coincidence concerning 163 and the Monster?

number-theory group-theory sequences-and-series

jul 27 '11 at 16:52 Willie Wong♦ 30.7k

votes

answers

views

Riemann zeta sums and harmonic numbers

sequences-and-series special-functions riemann-zeta

jun 24 '12 at 21:13 user17762 76.1k

votes

answer

234

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What is the next “Tribonacci-like” pseudoprime?

sequences-and-series elementary-number-theory prime-numbers fibonacci-numbers

may 22 '12 at 22:50 Steven Stadnicki 14.2k

votes

answers

146

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A typo in a formula of Ramanujan?

special-functions math-history gamma-function

may 7 '12 at 20:53 Robert Israel 86.3k

votes

answers

217

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The elliptic curve $y^2 = 23328x^3-890273x^2+14755570x-7^7$

number-theory reference-request elliptic-curves

apr 28 '12 at 14:51 Álvaro Lozano-Robledo 5,250

votes

answers

views

On Sixth Powers $x_1^6+x_2^6+\dots+x_6^6 = z^6$

elementary-number-theory diophantine-equations

may 15 at 21:09 Tito Piezas III 2,640

votes

answers

views

The Tribonacci constant and the Dragon

sequences-and-series special-functions fractals transcendental-numbers constants

may 14 at 17:14 Tito Piezas III 2,640

votes

answers

views

Generalizing Ramanujan's 6-10-8 Identity

elementary-number-theory diophantine-equations

may 6 at 4:17 Tito Piezas III 2,640

votes

answers

views

Hypergeometric formulas for the Rogers-Ramanujan identities?

special-functions modular-forms

jul 16 at 17:08 Tito Piezas III 2,640