$(m^2+n^2) \div (m+n)$

Number Theory Level 1

$1^2 + 2^2$ is not divisible by $1+2.$
$2^2 + 3^2$ is not divisible by $2+3.$
$3^2 +4^2$ is not divisible by $3+4.$
$4^2 + 5^2$ is not divisible by $4+5.$
$5^2 + 6^2$ is not divisible by $5+6.$

True or False?

If $m$ and $n$ are consecutive positive integers, then $m^2 + n^2$ is never divisible by $m+n$ .

(m2+n2)÷(m+n)(m^2+n^2) \div (m+n)(m2+n2)÷(m+n)

$(m^2+n^2) \div (m+n)$