scholarly journals On Terai's conjecture concerning Pythagorean numbers

2001 ◽  
Vol 100 (1) ◽  
pp. 41-45 ◽  
Author(s):  
Maohua Le
Keyword(s):  
Pythagorean Numbers ◽  
Terai’S Conjecture

scholarly journals On Terai's conjecture concerning Pythagorean numbers

2000 ◽  
Vol 61 (2) ◽  
pp. 329-334
Author(s):  
Maohu A. Le
Keyword(s):  
Pythagorean Numbers ◽  
Terai’S Conjecture ◽  
Positive Integers

In this paper we prove that if a, b, c, r are fixed positive integers satisfying a2 + b2 = cr, gcd(a, b) = 1, a ≡ 3(mod 8), 2 | b, r > 1, 2 ∤ r, and c is a (x,y,z) = (2, 2,r) satisfying x > 1, y > 1 and z > 1.

Tenth wave, the Pythagorean numbers, and the etymology of “ten”

1858 ◽  
Vol s2-V (114) ◽  
pp. 194-197
Author(s):  
Andrew Steinmetz
Keyword(s):  
Pythagorean Numbers

Jeśmanowicz’ Conjecture with Congruence Relations. II

2014 ◽  
Vol 57 (3) ◽  
pp. 495-505 ◽  
Author(s):  
Yasutsugu Fujita ◽  
Takafumi Miyazaki
Keyword(s):  
Positive Solution ◽  
Diophantine Equation ◽  
Congruence Relations ◽  
Pythagorean Numbers

AbstractLet a, b, and c be primitive Pythagorean numbers such that a2 + b2 = c2 with b even. In this paper, we show that if b0 ≡ ∊(mod a) with ε ∊ {±1} for certain positive divisors b0 of b, then the Diophantine equation ax + by = cz has only the positive solution (x, y, z) = (2, 2, 2).

Exceptional cases of Terai’s conjecture on Diophantine equations

2011 ◽  
Author(s):  
Takafumi Miyazaki ◽  
Masaaki Amou ◽  
Masanori Katsurada
Keyword(s):  
Diophantine Equations ◽  
Terai’S Conjecture

Pythagorean Numbers

1974 ◽  
Vol 67 (7) ◽  
pp. 667-669
Author(s):  
Israel Cohen
Keyword(s):  
Simple Method ◽  
Pythagorean Numbers

This article shows a simple method for finding the sets of integers that are the measures of sides of right triangles. It provides a method for the geometry teacher or students to generate right triangles.

Reflections, Rotations, and Pythagorean Numbers

2008 ◽  
Vol 19 (1) ◽  
pp. 1-14 ◽  
Author(s):  
G. Aragón-González ◽  
J. L. Aragón ◽  
M. A. Rodríguez-Andrade ◽  
L. Verde-Star
Keyword(s):  
Pythagorean Numbers
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