Question

if x^2+y^2 = z^2,
show that xy/2 is not a perfect square.

all are integers.

Answer 1

hmm

Answer 2

you have to show that x * y/2 cannot be the dimensions of a square if they satisfy this equation

Answer 3

in other words either x/2 = y or y/2=x

Answer 4

yess

Answer 5

WLOG, we can say that x and y do not share a common factor
\[2k^2=xy\]
We also know that x|k and y|k
So 2k^2/x is an [even] integer. Likewise 2k^2/y is an [even] integer. However, one of them must be odd.