One-Digit Number is Harshad
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Theorem
Let $n$ be a $1$-digit positive integer.
Then $n$ is a harshad number.
Proof
By definition, a harshad number is divisible by the sum of its digits base $10$.
Let $n$ be a $1$-digit positive integer.
The sum of the digits of $n$ is trivially $n$.
The result follows from Integer Divides Itself.
$\blacksquare$