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Can you find another prime?

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October 23, 2024
number theoryChile

Problem Statement

Let 133…33 133\ldots 33 be a number with k≥2 k \geq 2 digits, which we assume is prime. Prove that k(k+2) k(k + 2) is a multiple of 24. (For example, 133...33 is a prime number when k=16 k = 16
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