Pairs of consecutive 3-digit numbers in base b

 
 
For which base   b   there exist pairs of consecutive 3-digit numbers each equal to the sum of the cubes of their digits.

 

For example, in   b = 8

 

660   base-8   =   432   base-10
661   base-8   =   433   base-10

are each the sum of the cubes of their digits:

6^3 \; + \; 6^3 \; + \; 0^3 \; = \; 432
6^3 \; + \; 6^3 \; + \; 1^3 \; = \; 433

 

Find other pairs of consecutive 3-digit numbers

 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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