x^2 + y and y^2 + 17*x

 
 
Find positive integers   x, \; y   so that the expressions

x^2 \; + \; y    and   
y^2 \; + \; 17 \, x

are to be made squares.

 
Here are some solutions:
 

x^2 \; + \; y   …………………………..   y^2 \; + \; 17 \, x

1^2 + 8 = 3^2   ….. ………………..   8^2 + (17\times 1) = 9^2
3^2 + 7 = 4^2 = 2^4   ……………..   7^2 + (17\times 3) = 10^2
24^2 + 49 = 25^2 = 5^4   ……….   49^2 + (17\times 24) = 53^2
20^2 + 84 = 22^2   ………………   84^2 + (17\times 20) = 86^2
33^2 + 280 = 37^2   …………..   280^2 + (17\times 33) = 281^2

 
Any other solutions?
 

 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged . Bookmark the permalink.

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