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May 26th, 2016, 03:36 PM   #1
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Math Focus: Number theory
Cube vs. square

Is there a cube number and a square number whose difference is 5?
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May 26th, 2016, 10:02 PM   #2
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How about -1 and 4?
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May 26th, 2016, 10:07 PM   #3
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$A^3-B^2=5$

Or

$A^3-B^2=3^2-2^2$

with $(A, B)\in N$ ?
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May 26th, 2016, 10:53 PM   #4
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Quote:
Originally Posted by complicatemodulus View Post
$A^3-B^2=5$

Or

$A^3-B^2=3^2-2^2 \ \ \ \ \ \ $ This doesn't apply.

with $(A, B)\in N$ ?
No, 9 is a perfect square, not a perfect cube.
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May 26th, 2016, 11:42 PM   #5
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..sorry you think I'm soo stupid...

I'm just representing 5 as 9-4... the cube as A^3, and the square as A^2... and asking for math details about A & B... to avoid trivial answer -1 and 4....

of course the question can also be:

$A^2-B^3=5$

and again with $(A,B)\in ??$

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May 27th, 2016, 05:24 AM   #6
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And what about the number of solutions of such equation?

I mean: how many solutions $(x,y)$ there are for $y^3=\pm 5+x^2$

That is an easy one...
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May 27th, 2016, 05:57 AM   #7
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Quote:
Originally Posted by al-mahed View Post
And what about the number of solutions of such equation?

I mean: how many solutions $(x,y)$ there are for $y^3=\pm 5+x^2$

That is an easy one...
...and of couse pls let us know if $(x,y)\in N, Q$ or $R$.
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May 27th, 2016, 12:01 PM   #8
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Pardon,

Is there a cube of a whole number and a square of a whole number whose difference is 5?

-Loren
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May 27th, 2016, 12:40 PM   #9
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Quote:
Originally Posted by complicatemodulus View Post
..sorry you think I'm soo stupid...

I'm just representing 5 as 9-4... the cube as A^3, and the square as A^2... and asking for math details about A & B...
to avoid trivial answer -1 and 4....

of course the question can also be:

$A^2-B^3=5$

and again with $(A,B)\in ??$
No, I didn't judge you as "stupid" from that post of yours. I felt you posted something that was/is inconsistent
with what is supposed to be a perfect cube, followed by a subtraction sign, followed by a perfect square
on the opposite side of the equals sign.


Quote:
Originally Posted by Loren View Post
Pardon,

Is there a cube of a whole number and a square of a whole number whose difference is 5?

-Loren
Loren,

for a difference (as opposed to a sum), in general, X - Y is not equal to Y - X.

You mentioned "cube of a whole number" first and then "square of a whole number" second.

But I take it you are looking/intending for any solutions, regardless of whether the perfect
square comes first or second in the equation.

.
Thanks from Loren

Last edited by Math Message Board tutor; May 27th, 2016 at 12:52 PM.
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May 27th, 2016, 01:30 PM   #10
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Math Focus: Number theory
For instance,

1^3-1^2=0

3^2-2^3=1

3^3-5^2=2

2^2-1^3=3

5^3-11^2=4

Next: What perfect cube of a natural number differs from a perfect square of a natural number by a magnitude of 5?
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