Wolfram Demonstrations Project

What is the greatest positive integer

such that the Diophantine equation

has no solution in non-negative integers? If

and

are relatively prime numbers, the equation has a solution in integers for any integer

and has a solution in non-negative integers for any integer

greater than

J. J. Sylvester (1814–1897) posed the problem of finding the largest number that cannot be made up of some combination of 5p and 17p stamps.

Reference

[1] D. Wells, The Penguin Book of Curious and Interesting Puzzles, New York: Penguin Books, 1993 p. 64.

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Sylvester's Postage Stamp Problem