Question 1200168
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For reference
https://en.wikipedia.org/wiki/Pythagorean_triple
Euclid's formula, with respect to the pythagorean triples, refers to a set of 3 equations
<ul><li>a = m^2 - n^2</li><li>b = 2mn</li><li>c = m^2 + n^2</li></ul>m & n represent positive integers.
We must have m > n so that m^2-n^2 is positive. 
I'll let you confirm those equations satisfy a^2+b^2 = c^2



If m = 8 and n = 3, then,<ul><li>a = m^2 - n^2 = 8^2 - 3^2 = 64 - 9 = 55</li><li>b = 2mn = 2*8*3 = 48</li><li>c = m^2 + n^2 = 8^2 + 3^2 = 64 + 9 = 73</li></ul>This makes (55, 48, 73) one possible pythagorean triple out of infinitely many.


a = 55
a^2 = 55^2 = 3025
b = 48
b^2 = 48^2 = 2304
a^2+b^2 = 3025+2304 = 5329
c = 73
c^2 = 73^2 = 5329
This confirms a^2+b^2 = c^2 is true for (a,b,c) = (55,48,73).
The order of a & b doesn't matter. The c must be the longest side.
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