Definition :
Idoneal numbers are the positive integers $D$ such that any integer expressible in only one way as x^2 ± Dy^2 (where $x^2$ is relatively prime to $Dy^2$) is a prime, prime power, or twice one of these.
Number $32$ satisfies this definition because :
$p^2 = x^2+32 \cdot y^2$ if and only if : $p \equiv 1 \pmod {32}$ or $p \equiv 17 \pmod {32}$ , and every prime number
p is expressible in exactly one way as : $\sqrt{ x^2+32 \cdot y^2}$ ,where $\gcd(x^2,32 \cdot y^2)=1$ .
However , there is an additional condition on Idoneal numbers :
"A positive integer $D$ is idoneal iff it cannot be written as $ab+bc+ca$ for integer $a, b$, and $c$
with $0."
Since , $32 = 1 \cdot 2 + 2 \cdot 10 +1 \cdot 10$ number $32$ doesn't satisfy this condition and therefore it isn't Idoneal number .
My question : Why definition of Indoneal numbers is inconsistent with the $abc$ requirement in case of number $32$ ?