(a) How many ordered pairs 
of integers are there such that 
? Does the question have a geometric interpretation?
(b) How many ordered triples 
of integers are there such that 
? Does the question have a geometric interpretation?
By geometric interpretation we mean, "Is there a picture that describes the question?"
+33658 (a) All combinations of (±3,±4) and (±4,±3) satisfy the equation. Geometrically, these points lie on the circumference of a circle of radius 5.
(b) All combinations of (±2, ±3, ±6), (±2, ±6, ±3), (±6, ±2, ±3), (±6, ±3, ±2),(±3, ±2, ±6) and (±3, ±6, ±2) satisfy the equation. Geometrically, these points lie on a sphere of radius 7. See image below:
.
