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Thu 13 Mar, 2008 03:37 am
A pythagorean triple is a set of three integers x,y,z such that x^2+y^2=z^2; the triple is said to be primitive if gcd(x,y,z)=1. The values x,y,z are the lengths of the sides of a right angled triangle.
Example:
(3,4,5) has 3^2+4^2=9+16=25=5^2 and gcd(3,4,5)=1 so (3,4,5) is a primitive pythagorean triple.
(6,8,10) has 6^2+8^2=36+64=100=10^2 but gcd(6,8,10)=2 so (6,8,10) is a pythagorean triple but is not primitive.
Notes:
gcd=greatest common divisor.
integer=whole number (...,-2,-1,0,1,2,3,...)
Your problem:
Find a primitive pythagorean triple for which the triangle has an area of 666666.
To answer:let the sides be x,y,z enter your answer as xyz where x<y<z (so (3,4,5) would be 345 for example).
666666, 693, 1924, 2045}, Primitive!
(Wells 1986, p. 89).