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WOLFRAM|DEMONSTRATIONS PROJECT

Sylvester's Postage Stamp Problem

​
dots / numbers
highest nonsolvable / current equation
a
7
b
8
c
24
Current equation: 7x+8y = 24.
What is the greatest positive integer
c
such that the Diophantine equation
ax+by=c
has no solution in non-negative integers? If
a
and
b
are relatively prime numbers, the equation has a solution in integers for any integer
c
and has a solution in non-negative integers for any integer
c
greater than
ab-2
.
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