Integers (x,y) such that x – y and x*y are squares

 
 
There are pairs of numbers whose difference and product are perfect squares:

x \; - \; y \; = \; a^2
x \, y \; = \; b^2

Here are few examples where the smaller number of such a pair   y = 2, 3, 5, 7, 11, 13

 

18 - 2 = 4^2                         18\times 2 = 6^2
12 - 3 = 3^2                          12\times 3 = 6^2
405 - 5 - 20^2                      405\times 5 = 45^2
448 - 7 = 21^2                      448\times 7 = 56^2
1100 - 11 = 33^2                    1100\times 11 = 110^2
5475613 - 13 = 2340^2        5475613\times 13 = 8437^2

 
DIFF+PROD 1

 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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