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

.