What are the number of solutions in natural Numbers to the following linear equation in three variables...
3x+4y+5z=200
Can there be a general form for the number of solutions for this type of equation:
ax+by+cz=d
a,b,c,d,x,y,z belong to Natural Numbers
But finding the coefficeint of by counting, is equivalent to listing down all the solutions of the original equation and counting them up. How can I proceed to find the coefficient in a more efficient manner?