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Albert1
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let AB = y and AC= x

$y^2-x^2=n^2$
or$(y+x)(y-x) = n^2$
as n is prime

$y+x = n^2$ and $y-x=1$ as they cannot be both n

so $AB+AC = n^2$ and $AB+AC+BC=n^2+n$
 
kaliprasad said:
let AB = y and AC= x

$y^2-x^2=n^2$
or$(y+x)(y-x) = n^2$
as n is prime

$y+x = n^2$ and $y-x=1$ as they cannot be both n

so $AB+AC = n^2$ and $AB+AC+BC=n^2+n$
very nice!