“Pythagorean Quadruple”的概念、定义、习题解题方法及翻译-数学辞典

单词

Pythagorean Quadruple

释义

Pythagorean Quadruple

Positive Integers , , , and which satisfy

(1)

For Positive Even

and

, there exist such Integers

and

; for Positive Odd

and

, no such Integers exist (Oliverio 1996). Oliverio (1996) gives the following generalization of thisresult. Let

, where

are Integers, and let

be the number of OddIntegers in

. Then Iff

(mod 4), there exist Integers

and

such that

(2)

A set of Pythagorean quadruples is given by

			(3)
			(4)
			(5)
			(6)

where

, and

are Integers,

(7)

and

(8)

(Mordell 1969). This does not, however, generate all solutions. For instance, it excludes (36, 8, 3, 37). Another setof solutions can be obtained from

			(9)
			(10)
			(11)
			(12)

(Carmichael 1915).

See also Euler Brick, Pythagorean Triple

References

Carmichael, R. D. Diophantine Analysis. New York: Wiley, 1915.

Mordell, L. J. Diophantine Equations. London: Academic Press, 1969.

Oliverio, P. ``Self-Generating Pythagorean Quadruples and -tuples.'' Fib. Quart. 34, 98-101, 1996.

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