Difference between non negative integral solution and positive solution
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Difference between non - negative and positive integral solution :
(a) Number of non negative integral solution of equation x+2y+3z+4w=nx+2y+3z+4w=n = Coefficient of xnxn in [(1−x)−1(1−x2)−1(1−x3)−1(1−x4)−1][(1−x)−1(1−x2)−1(1−x3)−1(1−x4)−1]
(b) Number of positive integral solution of equation x+2y+3z+4w=nx+2y+3z+4w=n = Coefficient of xn−(1+2+3+4)xn−(1+2+3+4) in [(1−x)−1(1−x2)−1(1−x3)−1(1−x4)−1]
(a) Number of non negative integral solution of equation x+2y+3z+4w=nx+2y+3z+4w=n = Coefficient of xnxn in [(1−x)−1(1−x2)−1(1−x3)−1(1−x4)−1][(1−x)−1(1−x2)−1(1−x3)−1(1−x4)−1]
(b) Number of positive integral solution of equation x+2y+3z+4w=nx+2y+3z+4w=n = Coefficient of xn−(1+2+3+4)xn−(1+2+3+4) in [(1−x)−1(1−x2)−1(1−x3)−1(1−x4)−1]
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