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# Divisibility of Permutation of digits

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

Note by Yan Yau Cheng
2 years, 11 months ago

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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. · 2 years, 11 months 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? · 2 years, 7 months ago