September 8th, 2019, 08:31 PM  #1 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 458 Thanks: 29 Math Focus: Number theory  Close powers of integers
Do there exist powers of integer pairs, both greater than three, whose differences are greater than two and singly sequential? For differences zero to two: 1^N1^N=0...3^22^3=1...3^35^2=2... ? 
September 9th, 2019, 05:19 AM  #2 
Senior Member Joined: Jun 2019 From: USA Posts: 213 Thanks: 90 
Can you define that a little more clearly? You're looking for integers a and b: a>3, b>3, $\displaystyle a^bb^a>2$ Singly sequential meaning what? ab=1? 
September 10th, 2019, 01:23 PM  #3 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 458 Thanks: 29 Math Focus: Number theory  
September 11th, 2019, 06:44 AM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,683 Thanks: 2664 Math Focus: Mainly analysis and algebra 
Trivially when $b=d=1$. What are your constrains such as the greater than three and the differences greater than two?

September 11th, 2019, 02:09 PM  #5  
Senior Member Joined: May 2015 From: Arlington, VA Posts: 458 Thanks: 29 Math Focus: Number theory  Quote:
I guess these are the only constraints I need, noting the trivial case b=d=1. I know 1^b1^d=0, 3^22^3=1, and 3^35^2=2. Likewise negatives. Does this pattern extend to all Z?  

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