Number of form 28000...0007 is Divisible by 7/Proof 2
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Theorem
Let $x$ be a natural number in the form:
- $\sqbrk {28 \underbrace {000 \cdots 0}_n 7}_{10}$
Then $x$ is divisible by $7$.
Proof
We have:
\(\ds \sqbrk {28 \underbrace {000 \cdots 0}_n 7}_{10}\) | \(=\) | \(\ds 7 \times \sqbrk {4 \underbrace {000 \cdots 0}_n 1}_{10}\) |
and the result follows by definition of divisibility.
$\blacksquare$