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Please show all working out in as much detail as possible, thanks
3) Denote by an the number, which in decimale expansions has the form 111 times). So, al 1, a2 11, аз 111, a4 1111 etc. Let p be a prime number, which is different from 2 and 5. Prove that there exist n 22, such that p divides an. (Hint: Based on the fact that Z/pZ is finite, show that anpp for n # m)

3) Denote by an the number, which in decimale expansions has the form 111 times). So, al 1, a2 11, аз 111, a4 1111 etc. Let p be a prime number, which is different from 2 and 5. Prove that there exist n 22, such that p divides an. (Hint: Based on the fact that Z/pZ is finite, show that anpp for n # m)

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Question: please show all working out in as much detail as...

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