Question

Prove that if the legs of a right-angle triangle are are expressible as the squares of integers, the hypotenuse cannot be an integer.

Answer 1

fermat's last theorem?

@jim_thompson5910

Answer 2

not exactly sure what the question is asking

Answer 3

if you have something like a right triangle with side lengths of 3, 4, 5 then this is false

Answer 4

but 3 is not a square of an integer

Answer 5

oh i see

Answer 6

Let's assume that we have a triangle with side lengths a, b, c where

a = p^2
b = q^2
c = r^2

this would mean

a^2 + b^2 = c^2

(p^2)^2 + (q^2)^2 = (r^2)^2

p^4 + q^4 = r^4

but yes as completeidiot is saying, there are no integral solutions to this equation by Fermat's Last Theorem

Answer 7

no i was wondering whether or not it would be applicable

because it doesnt state that the hypothenuse must be a square as well

Answer 8

oh true, they just state that the hypotenuse isn't an integer at all..hmm

Answer 9

here is one interesting fact


on this page
http://en.wikipedia.org/wiki/Pythagorean_triple#Elementary_properties_of_primitive_Pythagorean_triples


it says that "At most one of a, b, c is a square. (See Infinite descent#Non-solvability of r2 + s4 = t4 for a proof.)"