Math Trivia : How to make Pythagorean numbers

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How to make Pythagorean numbers 

Samos Island where Pythagoras was born


In the case of X^2 + Y^2 = Z^2  (X^2 means X*X.), 

X,Y,Z are Pythagorean numbers.


Chord(Pythagorean Tuning)


<Idea 1>

Find two numbers Y and Z whose sum is equal to the square of an odd number X and whose difference is 1, then X, Y, and Z are Pythagorean numbers.

7^2=7*7=49

49=24+25

7,24,25 are Pythagorean numbers.


Samos island in the Aegean Sea


<Idea 2>

X=2*A, Y=A^2-1, Z=A^2+1 (A=2,3,…), 

then X, Y, Z are Pythagorean numbers.

A=4

X=2*A=8

Y=4^2-1=15

Z=4^2+1=17