What is primitive pythagorean triple?

Question

I'm learning pythagorean thereom and I don't understand what a primitive pythagorean is. if you can explain it simple that would be great

how would you find it?

Answer 1

A pythagorean triple is a group of three positive integers a,b and c such that a^2 + b^2 = c^2.
A primitive pythagorean triple the same as a pythagorean triple except it has the additional feature that a, b, and c don't have any common factors except one.

Answer 2

Pythagoras's Theorem states that if a right-angled triangle has hypotenuse c and perpendicular sides a and b then
a^2 + b^2 = c^2. If a, b and c are integers then a, b, c form a Pythagorean triple. For example 3, 4, 5 is a pythagorean triple because 3^2 +4^2 = 9 + 16 = 25 = 5^2. Now 6, 8, 10 is also a pythagorean triple but is not a primitive one because it is simply twice 3, 4, 5. The latter is primitive because they form the smallest triple of that shape while still remaining integers.
Other primitive Pythagorean triples are;
5, 12, 13
7, 24, 25
9, 40, 41
11, 60, 61
13, 84, 85
and so on. Notice that the sum of the second and third numbers is the square of the first number. Thus given any odd integer N, square it and find the two consecutive integers whose sum is N^2. In the third example above we choose 9, square it to obtain 81 and the two consecutive integers adding up to 81 are 40 and 41, so 9, 40, 41 is a primitive Pythagorean triple.

Answer 3

a primitive phythagorean triple is a set of three whole numbers
a, b, and c

where a^2 + b^2 = c^2 (the pythagorean triple part!!!!)

AND

a, b and c have no common divisor except 1 (the primitive part!!!!)

Answer 4

basicly, the only way for a right triangle to be real is if the hypotnuse(sp?), raised to the second power, to equal the legnth of the first leg, squared, pluse the legnth of the second leg, also squared. which is seen as
a^2+b^2=c^2.

there is a special one in which the ratios of the legs are, as a:b:c, seen as 3:4:5, and are the easiest ones to solve, if you see any of the values are multiples of a number, and one of the above number, in which there is also another, with the same number, times another of them, you have the answer to the final side.