Valuations, arithmetic progressions, and prime numbers
classification
🧮 math.NT
keywords
arithmeticgiveprimeprogressionstheoremdivergenceeuler-legendreinfinitude
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In this short note, we give two proofs of the infinitude of primes via valuation theory and give a new proof of the divergence of the sum of prime reciprocals by Roth's theorem and Euler-Legendre's theorem for arithmetic progressions.
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