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Congruent Number

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A congruent number can be defined as an integer that is equal to the area of a rational right triangle (Koblitz 1993).

Numbers (a,x,y,z,t) such that

{x^2+ay^2=z^2; x^2-ay^2=t^2
(1)

are also known as congruent numbers. They are a generalization of the congruum problem, which is the case y=1.

For example, a=101, the smallest congruent numbers are

x=2015242462949760001961
(2)
y=118171431852779451900
(3)
z=2339148435306225006961
(4)
t=1628124370727269996961.
(5)

See also

Congruum, Rational Triangle

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References

Guy, R. K. "Congruent Number." §D76 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 195-197, 1994.Koblitz, N. Introduction to Elliptic Curves and Modular Forms. New York: Springer-Verlag, 1993.

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Congruent Number

Cite this as:

Weisstein, Eric W. "Congruent Number." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CongruentNumber.html

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