Question 9210: The square of the largest of three consecutive integers is equal to the sum of the squares of the other two. Find the integers
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! Wrong category of posting again.
This kind of numbers are called Pythagorean triple, they form the sides
of right triangles and that what you should know geometrically.
The smallest such triple is (3,4, 5)
In general,if a^2 +b^2 = c^2 where a,b,c are positive integers
they the general solutions as (solved in old Greek times )
a = u^2 - v^2
b = 2uv
c = u^2 + v^2 where u , v distnct positive integers.
[Of course,u should be greater than v]
Hence,you can see there are infinitely many such triples.
as (5,12, 13),..... etc
Kenny
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