+0

(a) How many ordered pairs of integers are there such that ? Does the question have a geometric interpretation?

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1300
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(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

#2
+85759
+19

Alan...in the first one, don't (±5, 0) and (0,±5) also "work ??"

And in the second....don't  (±7, 0, 0), (0,±7, 0 ) and (0, 0, ±7) also do the job??

CPhill  Mar 29, 2015
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#1
+26640
+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:

.

Alan  Mar 29, 2015
#2
+85759
+19

Alan...in the first one, don't (±5, 0) and (0,±5) also "work ??"

And in the second....don't  (±7, 0, 0), (0,±7, 0 ) and (0, 0, ±7) also do the job??

CPhill  Mar 29, 2015
#3
+26640
+11

Yes, I guess they do.  I forgot about the zeros!

In both cases these points will still lie on the circle of radius 5/sphere of radius 7.

.

Alan  Mar 29, 2015

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