The number of solutions in positive integers of 2x + 3y = 763 is:
Solving 2x + 3y = 763 for x, we have x
=
.
Since x is a positive integer, 763 - 3y must be a positive even
number, so that y must be a positive odd integer, such that
.
There are 254 multiples of 3 less than 763, half of which are even
multiples and half, odd multiples. Therefore, there are 127 possible
solutions to the given equation under the stated conditions.