Question

Prove that every prime number is the leg of exactly one right triangle with integer sides.

~I've noticed that pythagorean triples usually contain atleast one prime number, but I am not exactly sure how you would go about proving that.

Answer 1

yes!

Answer 2

found it?

Answer 3

No...

Answer 4

oh. Ok one second

Answer 5

Euclid's formula[1] is a fundamental formula for generating Pythagorean triples given an arbitrary pair of positive integers m and n with m > n. The formula states that the integers
maybe we can use this

Answer 6

oops it didn't copy the formulas

Answer 7

a=m^2-n^2
b=2mn
c=m^2+n^2

Answer 8

So when using this formula would we be subbing in prime numbers for m and n?

Answer 9

a=k(m^2-n^2)
b=k(2mn)
c=k(m^2+n^2)

k is a positive integer
no m and n are integers (can be anything)

Answer 10

Okay~ i think I'm following you..

Answer 11

like i said i'm not sure if we will need this our not
im still thinking

Answer 12

http://mathforum.org/library/drmath/view/67289.html

this might help