TITLE: Intuition behind counterexample of Euler's sum of powers conjecture
QUESTION [22 upvotes]: I was stunned when I first saw the article Counterexample to Euler's conjecture on sums of like powers by L. J. Lander and T. R. Parkin:.

How was it possible in 1966 to go through the sheer astronomical space of possibilities, on a CDC 6600 computer?

1) Did Lander and Parkin reveal their strategy?
2) How would you, using all the knowledge that was accessable until 1965, go to search for counter-examples, if you have access to a computer with 3 MegaFLOPS?

(As a comparison, todays home computers can have beyond 100 GigaFLOPS, using GPUs even TeraFLOPs)

REPLY [2 votes]: The longer and more detailed paper reveals that where possible, various modulo constraints were used to shrink the number of tuples to search through further:
L. J. Lander; T. R. Parkin; J. L. Selfridge (1967). "A Survey of Equal Sums of Like Powers". Mathematics of Computation. 21 (99): 446–459. doi:10.1090/S0025-5718-1967-0222008-0