Question 17
How many solutions $$\left(x, y, z\right)$$ of the equation $$x+y^{2}+z^{3}=50$$ exist, where x, y and z are positive integers?
Solution
$$x+y^2+z^3=50$$
Let z = 1, $$x+y^2=49$$
Pairs of (x,y) = (48,1),(45,2),(40,3),(33,4),(24,5),(13,6) = 6 solutions
Let z = 2, $$x+y^2=42$$
Pairs of (x,y) = (41,1),(38,2),(33,3),(26,4),(17,5),(6,6) = 6 solutions
Let z = 3,$$x+y^2=23$$
Pairs of (x,y) = (22,1),(19,2),(14,3),(7,4) = 4 solutions
Total possible solutions = 16
$$\therefore\ $$ The required answer is C.
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