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 May 26th, 2016, 03:36 PM #1 Senior Member   Joined: May 2015 From: Arlington, VA Posts: 472 Thanks: 29 Math Focus: Number theory Cube vs. square Is there a cube number and a square number whose difference is 5?
 May 26th, 2016, 10:02 PM #2 Global Moderator   Joined: Dec 2006 Posts: 21,132 Thanks: 2340 How about -1 and 4? Thanks from 123qwerty
 May 26th, 2016, 10:07 PM #3 Banned Camp   Joined: Dec 2012 Posts: 1,028 Thanks: 24 $A^3-B^2=5$ Or $A^3-B^2=3^2-2^2$ with $(A, B)\in N$ ?
May 26th, 2016, 10:53 PM   #4
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Quote:
 Originally Posted by complicatemodulus $A^3-B^2=5$ 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.

 May 26th, 2016, 11:42 PM #5 Banned Camp   Joined: Dec 2012 Posts: 1,028 Thanks: 24 ..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 $(A,B)\in ??$ Thanks Ciao Stefano
 May 27th, 2016, 05:24 AM #6 Senior Member   Joined: Dec 2007 Posts: 687 Thanks: 47 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...
May 27th, 2016, 05:57 AM   #7
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Quote:
 Originally Posted by al-mahed 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 $R$.

 May 27th, 2016, 12:01 PM #8 Senior Member   Joined: May 2015 From: Arlington, VA Posts: 472 Thanks: 29 Math Focus: Number theory Pardon, Is there a cube of a whole number and a square of a whole number whose difference is 5? -Loren
May 27th, 2016, 12:40 PM   #9
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Quote:
 Originally Posted by complicatemodulus ..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 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.

.

Last edited by Math Message Board tutor; May 27th, 2016 at 12:52 PM.

 May 27th, 2016, 01:30 PM #10 Senior Member   Joined: May 2015 From: Arlington, VA Posts: 472 Thanks: 29 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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