“Diophantine Equation nth Powers”的概念、定义、习题解题方法及翻译-数学辞典

单词

Diophantine Equation nth Powers

释义

Diophantine Equation nth Powers

The 2-1 equation

(1)

is a special case of Fermat's Last Theorem and so has no solutions for

. Lander et al. (1967) give a table showing the smallest

for which a solution to

with

is known.

Take the results from the Ramanujan 6-10-8 Identity that for , with


	(2)

and


	(3)

then

(4)

Using

			(5)
			(6)

now gives

(7)

for

or 4.

See also Ramanujan 6-10-8 Identity

References

Berndt, B. C. Ramanujan's Notebooks, Part IV. New York: Springer-Verlag, p. 101, 1994.

Berndt, B. C. and Bhargava, S. ``Ramanujan--For Lowbrows.'' Amer. Math. Monthly 100, 644-656, 1993.

Dickson, L. E. History of the Theory of Numbers, Vol. 2: Diophantine Analysis. New York: Chelsea, pp. 653-657, 1966.

Gloden, A. Mehrgradige Gleichungen. Groningen, Netherlands: P. Noordhoff, 1944.

Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, 1994.

Lander, L. J.; Parkin, T. R.; and Selfridge, J. L. ``A Survey of Equal Sums of Like Powers.'' Math. Comput. 21, 446-459, 1967.

Reznick, B. ``Sums of Even Powers of Real Linear Forms.'' Mem. Amer. Math. Soc. No. 463, 96. Providence, RI: Amer. Math. Soc., 1992.

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