(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?"*

Guest Mar 29, 2015

#1**+10 **

(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:

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Alan
Mar 29, 2015