porve or disprove. product of 3 numbers of phythogorean triplet is dvisvible by 60?

Answer 1

For any positive integers a < b, b² - a², 2ab, and b² + a² are Pythagorean triplets. The product then would be:

2ab(b + a)(b - a)(b² + a²)

60 is factorized into 2² 3 5

If either a or b is even, then we already have 2². If both are odd, we still have 2² because of terms like (b + a), and because there's already a 2 at the beginning of the product expression. If either a or b is a multiple of 3, we have the 3 factor. Otherwise, either a or b is of the form 3x + 1 or 3x - 1, which means either the term (b + a) or (b - a) will be a muliple of 3. Finally, if either a or b is a muliple of 5, we have the 5 factor. Otherwise, either a or b is of the form 5x -2, 5x - 1, 5x + 1, 5x + 2. If both have either + or - 1, or + or - 2, then the term (b + a) or (b - a) will be a muliple of 5. Otherwise, if one has + or - 1 while the other has + or - 2, then the last term (b² + a²) will be a multiple of 5, and the proof is done.

Answer 2

It's true (and it was known to the Greeks), but I don't remember how the proof goes. It's also true that the product of the legs of an integer Phythgorean triple is divisible by 12.

There's gotta be a bunch of sites that explain the proof.


Doug

Answer 3

Appears to be TRUE.

PROVE;

a^2 + b^2 = c^2
If the Pythagroean triple has divisors
60 = 2 *2* 3 *5

Answer 4

What does porve mean?
What is the function of the full stop?
dvisvible is a good one.
Surely, even mathematicians learn some English.