(gcd(a, b))^2 = a + b

 
 
( \,gcd \,(a, b) \,)^2 \; = \; a \; + \; b

 

For example,
 

( \,gcd \,(2, 2) \,)^2 \; = \; 4 \; = \; 2 \; + \; 2

( \,gcd \,(6, 3) \,)^2 \; = \; 9 \; = \; 6 \; + \; 3

( \,gcd \,(12, 4) \,)^2 \; = \; 16 \; = \; 12 \; + \; 4

( \,gcd \,(20, 5) \,)^2 \; = \; 25 \; = \; 20 \; + \; 5
( \,gcd \,(15, 10) \,)^2 \; = \; 25 \; = \; 15 \; + \; 10

( \,gcd \,(30, 6) \,)^2 \; = \; 36 \; = \; 30 \; + \; 6

( \,gcd \,(42, 7) \,)^2 \; = \; 49 \; = \; 42 \; + \; 7
( \,gcd \,(35, 14) \,)^2 \; = \; 49 \; = \; 35 \; + \; 14

( \,gcd \,(56, 8) \,)^2 \; = \; 64 \; = \; 56 \; + \; 8
( \,gcd \,(40, 24) \,)^2 \; = \; 64 \; = \; 40 \; + \; 24

( \,gcd \,(72, 9) \,)^2 \; = \; 81 \; = \; 72 \; + \; 9
( \,gcd \,(63, 18) \,)^2 \; = \; 81 \; = \; 63 \; + \; 18

( \,gcd \,(90, 10) \,)^2 \; = \; 100 \; = \; 90 \; + \; 10
( \,gcd \,(70, 30) \,)^2 \; = \; 100 \; = \; 70 \; + \; 30

 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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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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