Question: Please write the solution step by step clearly, and the related material is Number Theory. I will give a like if it's understandable and correct.

Please write the solution step by step clearly, and the related material is Number Theory. I will give a like if it's understandable and correct. Thank you!

Show that for all n N there exists some x N such that each of the numbers x, x + 1, . . . , x + n 1 is divisible by some square of a prime.

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