Congruent Numbers

A set of numbers $(a, x, y, t)$ such that

$$\cases{ x^2+ay^2=z^2\cr x^2-ay^2=t^2.\cr}$$

They are a generalization of the Congruum Problem, which is the case $y=1$. For $a=101$, the smallest solution is

$$x = 2015242462949760001961$$

$$y = 118171431852779451900$$

$$z = 2339148435306225006961$$

$$t = 1628124370727269996961.$$

See also Congruum

References

Guy, R. K. ``Congruent Number.'' §D76 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 195-197, 1994.