Congruence equations of $ax^i+by^j\equiv c$ and $ax^i+by^j +d z^t \equiv c(\hbox {\rm mod}\, p)$ when $p=2q+1$ with $p$ and $q$ odd primes

Daeyeoul Kim; Ja Kyung Koo; Myung-Hwan

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Commun. Korean Math. Soc. 2005; 20(3): 467-485

Printed September 1, 2005

Congruence equations of $ax^i+by^j\equiv c$ and $ax^i+by^j +d z^t \equiv c(\hbox {\rm mod}\, p)$ when $p=2q+1$ with $p$ and $q$ odd primes

Daeyeoul Kim, Ja Kyung Koo, Myung-Hwan

Chonbuk National University, Korea Advanced Institute of Science and Technology, Seoul National Univ.

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Abstract

Let $p$ and $q$ be odd primes with $p=2q+1$. We study the number of solutions of congruence equations $ax^i +by^j \equiv c \pmod p$ and $ax^i +by^j +dz^t \equiv c \pmod p$

Keywords: congruences, counting solutions of Diophantine equations

MSC numbers: 11A07, 11D45

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Congruence equations of $ax^i+by^j\equiv c$ and $ax^i+by^j +d z^t \equiv c(\hbox {\rm mod}\, p)$ when $p=2q+1$ with $p$ and $q$ odd primes

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Congruence equations of $ax^i+by^j\equiv c$ and $ax^i+by^j +d z^t \equiv c(\hbox {\rm mod}\, p)$ when $p=2q+1$ with $p$ and $q$ odd primes

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Communications of the
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