2025/034) If p can be expressed as sum of 2 squares say $p = x^2+y^2$ then express 2p ,5p, 19p as sum of 2 squares

If p can be expressed as sum of 2 squares as below

$p =  x^2+y^2$

We know $2= 1^2 + 1^2$

Now using the identity 

$(a^2+b^2)(x^2 + y^2) = (ax+by)^2 + (bx-ay)^2$ (we can expand and see the result

We get $2p = (x+y)^2+ (x-y)^2$

Further $5 = 2^2 + 1^2$

So we get $5p = (2x+y)^2 + (x-2y)^2$

But 19 is of the form 4n + 3 and it cannot be expressed as sum of 2 squares so 19p cannot be expressed as sum of 2 squares