Archimedes began his challenge “If thou art diligent and wise, O stranger,
compute the number of cattle of the Sun.” The stipulations for the number of
cattle follow in four stanzas. The problem reduces to Pell’s equation and a
CRAY-1 supercomputer finally solved it in 1981.
We will trace the history of Pell’s Equation from around 200 B.C. when
Archimedes posed the cattle problem to 600 A.D. when the Indian mathematician
Brahmagupta first studied the equation rigorously to the 18th century when
Euler and Lagrange tackled the problem with continued fractions.