Pythagorean triples of the form (x, y, y+50)

 
 
x \; = \; 10 \,(10 \, n + 1)
y \; = \; (10 \, n + 1)^2 \; - \; 25
z \; = \; (10 \, n + 1)^2 \; + \; 25

x \; = \; 10 \,(10 \, n + 3)
y \; = \; (10 \, n + 3)^2 \; - \; 25
z \; = \; (10 \, n + 3)^2 \; + \; 25

x \; = \; 10 \,(10 \, n + 7)
y \; = \; (10 \, n + 7)^2 \; - \; 25
z \; = \; (10 \, n + 7)^2 \; + \; 25

x \; = \; 10 \,(10 \, n + 9)
y \; = \; (10 \, n + 9)^2 \; - \; 25
z \; = \; (10 \, n + 9)^2 \; + \; 25

x \; = \; 20 \, (5 \, n + 1)
y \; = \; 100 \, (n + 1/5)^2 \; - \; 25
z \; = \; 100 \, (n + 1/5)^2 \; + \; 25

x \; = \; 20 \, (5 \, n + 2)
y \; = \; 100 \, (n + 2/5)^2 \; - \; 25
z \; = \; 100 \, (n + 2/5)^2 \; + \; 25

x \; = \; 20 \, (5 \, n + 3)
y \; = \; 100 \, (n + 3/5)^2 \; - \; 25
z \; = \; 100 \, (n + 3/5)^2 \; + \; 25

x \; = \; 20 (5 \, n + 4)
y \; = \; 100 \, (n + 4/5)^2 \; - \; 25
z \; = \; 100 \, (n + 4/5)^2 \; + \; 25

x \; = \; 50 \, (2 \, n + 1)
y \; = \; 25 \, (2 \, n + 1)^2 \; - \; 25
z \; = \; 25 \, (2 \, n + 1)^2 \; + \; 25

x \; = \; 100 \, n
y \; = \; 100 \, n^2 \; - \; 25
z \; = \; 100 \, n^2 \; + \; 25

 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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