about Pythagorean quadruples - Mathematics Stack Exchange
WEBFor a is even and b is odd or b is even and a is odd; (1) Let us take a = 12 and b = 15 then m = 369 = 32 X 41 then ε = 1, 32 but ε = 41 is not possible as ε2 > m. Now for c = 184 and d = 185 for ε = 1; for c = 16 and d = 25 when 32 = ε; So the primitive quadruples for a = 12 and b = 15 are (12, 15, 184, 185) and also (12, 15, 16, 25).
Pythagorean Quadruples: - Mathematics Stack Exchange
WEBAll the primitive Pythagorean Quadruples are known. This is Theorem 3 on page 176 and Theorem 4 on page 177 of Jones_Pall_1939.pdf, available at TERNARY as a pdf. The same information is on the first two pages of Pall_Automorphs_1940.pdf at the same site.
Are there any large lists of pythagorean quadruples? : r/askmath
WEBNov 2, 2014 · Here you go, a full list of all pythagorean quadruples where a,b,c <= 100. If you want more, let me know, I can easily change my program to find more. This list does not include doubles by the way, so (1,4,8,9) is in there but (4,1,8,9) isn't because it's basically the same. HappyRectangle.
Pythagorean quadruples - Mathematics Stack Exchange
WEB$\begingroup$ A proof of a very similar expression of Pythagorean quadruples is given in Andreescu et al.: An Introduction to Diophantine Equations, Theorem 2.2.3, p.79 . (They use the parametrization based on the two numbers from the …
elementary number theory - Pythagorean Quadruples (Integer …
WEBJul 24, 2022 · A Pythagorean quadruple is the combination of two Pythagorean triples where the left two digits are the legs of a triple whose hypotenuse (which must be odd) matches the "odd" leg of a triple containing the right two digits. i,e $\space(3,4,5)\land(5,12,13)\longrightarrow (x,y,z,m)=(3,4,12,13).\quad$ As such, your statement that $\space x,y ...
Pythagorean "like" quadruples, help with general solutions.
WEBJan 29, 2023 · Pythagorean Quadruples (Integer Question) 3. Understanding specific explanation of centre value of 3x3 ...
About some Pythagorean Quadruples - Mathematics Stack Exchange
WEBAll the primitive Pythagorean Quadruples are known. This is Theorem 3 on page 176 and Theorem 4 on page 177 of Jones_Pall_1939.pdf, available at TERNARY as a pdf. The same information is on the first two pages of Pall_Automorphs_1940.pdf at the same site.
elementary number theory - Pythagorean quadruple sum and …
WEBOct 1, 2023 · Find all (possibly non-primitive) Pythagorean quadruples such that 9 times the square of the sum of its four elements is equal to twice the product of its three smallest elements. Stated algebraically, find all natural numbers x,y,z satisfying. $$2xyz = 9(x + y + z + \sqrt{x^2 + y^2 + z^2})^2$$
Is this a discovery or something known? "You find any Integer …
WEBOct 9, 2022 · If you take a quaternion number lets call it Q (Q=a+bi+cj)) Q² definitely generate a pythagorean quadruple and Q=a+bi+cj+dk will definitely generate pythagorean quintuple ex: Q=1+1i+1j+k, Q² = (-2)+2i+2j+2k, and 2²+2²+2²+2²=16 and 16 is 4² and this is true for any integers a,b,c,d
elementary number theory - Is there a tree of Pythagorean …
WEBFeb 17, 2021 · 2. It is well-known that there is a trinary tree that contains every primitive Pythagorean triple exactly once. It even has a Wikipedia page. Is there a similar tree that contains each primitive Pythagorean quadruple exactly once? It even has a math.SE answer, with more math the the Wikipedia page. See …