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# On infinitude of primes

Abstract : Let $K (>1)$ and $k (>1)$ be given integers. In this paper we prove that $e_K(q)\equiv0 \mod k^{[m]}$ for infinitely many primes $q$, where $m=c_k\log\log q$ for a certain $c_k>0$ and $e_K(q)$ denotes the exponent of $K$ modulo $q$. In particular, $q\equiv1 \mod k$ for infinitely many primes $q$.
Document type :
Journal articles
Domain :

https://hal.archives-ouvertes.fr/hal-01104356
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Submitted on : Friday, January 16, 2015 - 3:40:15 PM
Last modification on : Monday, March 28, 2022 - 8:14:08 AM
Long-term archiving on: : Friday, September 11, 2015 - 6:58:59 AM

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7Article5.pdf
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### Citation

S Srinivasan. On infinitude of primes. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 1984, Volume 7 - 1984, pp.21 - 26. ⟨10.46298/hrj.1984.112⟩. ⟨hal-01104356⟩

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