Final answer:
The question is about finding the general and least positive integral solutions for a linear Diophantine equation of the form 8x - 27y = d. The general solution involves using the Extended Euclidean Algorithm to find integers that satisfy the equation 8a - 27b = 1.
Step-by-step explanation:
The question appears to be incomplete as it discusses finding a general solution in integers for the equation 8x-27y, but the equation is not provided in full.
Assuming the student is referring to a Diophantine equation of the form 8x - 27y = d, where d is some integer, the general solution for x and y in integers would involve finding particular solutions and then using the theory of linear Diophantine equations to generate the general solution.
This often involves using the Extended Euclidean Algorithm to find integers a and b such that 8a - 27b = gcd(8,27), with gcd representing the greatest common divisor. Since gcd(8,27) = 1, the equation has solutions for every integer d, and the solutions can be found by multiplying the particular solution by d.