May 26th, 2016, 02:36 PM  #1 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 435 Thanks: 28 Math Focus: Number theory  Cube vs. square
Is there a cube number and a square number whose difference is 5?

May 26th, 2016, 09:02 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,831 Thanks: 2160 
How about 1 and 4?

May 26th, 2016, 09:07 PM  #3 
Banned Camp Joined: Dec 2012 Posts: 1,028 Thanks: 24 
$A^3B^2=5$ Or $A^3B^2=3^22^2$ with $(A, B)\in N$ ? 
May 26th, 2016, 09:53 PM  #4 
Banned Camp Joined: Jun 2014 From: Earth Posts: 945 Thanks: 191  
May 26th, 2016, 10:42 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 94... 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: $A^2B^3=5$ and again with $(A,B)\in ??$ Thanks Ciao Stefano 
May 27th, 2016, 04:24 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, 04:57 AM  #7 
Banned Camp Joined: Dec 2012 Posts: 1,028 Thanks: 24  
May 27th, 2016, 11:01 AM  #8 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 435 Thanks: 28 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, 11:40 AM  #9  
Banned Camp Joined: Jun 2014 From: Earth Posts: 945 Thanks: 191  Quote:
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:
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 11:52 AM.  
May 27th, 2016, 12:30 PM  #10 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 435 Thanks: 28 Math Focus: Number theory 
For instance, 1^31^2=0 3^22^3=1 3^35^2=2 2^21^3=3 5^311^2=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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