# Non-Wieferich primes in number fields and $abc$-conjecture

Srinivas Kotyada; Subramani Muthukrishnan

Czechoslovak Mathematical Journal (2018)

- Volume: 68, Issue: 2, page 445-453
- ISSN: 0011-4642

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topKotyada, Srinivas, and Muthukrishnan, Subramani. "Non-Wieferich primes in number fields and $abc$-conjecture." Czechoslovak Mathematical Journal 68.2 (2018): 445-453. <http://eudml.org/doc/294271>.

@article{Kotyada2018,

abstract = {Let $K/\mathbb \{Q\}$ be an algebraic number field of class number one and let $\mathcal \{O\}_K$ be its ring of integers. We show that there are infinitely many non-Wieferich primes with respect to certain units in $\mathcal \{O\}_K$ under the assumption of the $abc$-conjecture for number fields.},

author = {Kotyada, Srinivas, Muthukrishnan, Subramani},

journal = {Czechoslovak Mathematical Journal},

keywords = {Wieferich prime; non-Wieferich prime; number field; $abc$-conjecture},

language = {eng},

number = {2},

pages = {445-453},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Non-Wieferich primes in number fields and $abc$-conjecture},

url = {http://eudml.org/doc/294271},

volume = {68},

year = {2018},

}

TY - JOUR

AU - Kotyada, Srinivas

AU - Muthukrishnan, Subramani

TI - Non-Wieferich primes in number fields and $abc$-conjecture

JO - Czechoslovak Mathematical Journal

PY - 2018

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 68

IS - 2

SP - 445

EP - 453

AB - Let $K/\mathbb {Q}$ be an algebraic number field of class number one and let $\mathcal {O}_K$ be its ring of integers. We show that there are infinitely many non-Wieferich primes with respect to certain units in $\mathcal {O}_K$ under the assumption of the $abc$-conjecture for number fields.

LA - eng

KW - Wieferich prime; non-Wieferich prime; number field; $abc$-conjecture

UR - http://eudml.org/doc/294271

ER -

## References

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