Divisibility of Permutation of digits

Show that all numbers whose digits are a permutation of 1234567890 are not prime.

#JOMO #JOMO2

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Sum of all the digits is 45. So no matter whichever number is formed by permutation of the given digits, it will be always divisible by 3. Hence the number will never be a prime.

Sudeep Salgia - 7 years, 1 month ago

Can you please tell me how to determine if a numbe of the form $a^n - 1$ is a prime or not, where $a$ is a fixed natural number and $n$ is any natural number?

Shabarish Ch - 6 years, 10 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$