Results 161 to 170 of about 3,530,646 (225)

A NOTE ON THE DIOPHANTINE EQUATION $x^{2}+(2c-1)^{m}=c^{n}$

Bulletin of the Australian Mathematical Society, 2018
Let $c\geq 2$ be a positive integer. Terai [‘A note on the Diophantine equation $x^{2}+q^{m}=c^{n}$ ’, Bull. Aust. Math. Soc. 90 (2014), 20–27] conjectured that the exponential Diophantine equation $x^{2}+(2c-1)^{m}=c^{n}$ has only the positive integer ...
MOU-JIE Deng, Jin Guo, Aidong Xu
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OntheExponential Diophantine Equation

Journal of Advanced Research in Applied Mathematics and Statistics
. Suppose that n is a positive integer. We show that the only positive integer solutions ( n, x, y, z ) of the exponential Diophantine equation ( n x y , n xyz are (3 , 2 , 1 , 2) , (3 , 1 , 2 , 3) .
Dinesh Thakur
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A Diophantine Equation Related to the Sum of Squares of Consecutive k -Generalized Fibonacci Numbers

The Fibonacci quarterly, 2014
Let (Fn)n≥0 be the Fibonacci sequence given by Fn+2 = Fn+1 + Fn, for n ≥ 0, where F0 = 0 and F1 = 1. There are several interesting identities involving this sequence such as F 2 n +F 2 n+1 = F2n+1, for all n ≥ 0.
Ana Paula Chaves, D. Marques
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Quadratic diophantine equations

Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1960
Tartakowsky (1929) proved that a positive definite quadratic form, with integral coefficients, in 5 or more variables represents all but at most finitely many of the positive integers not excluded by congruence considerations. Tartakowsky’s argument does not lead to any estimate for a positive integer which, though not so excluded, is not represented ...
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Diophantine Equations

2008
Abstract As an appetizer, here is a typical problem of the kind Sections 1–5 should equip you to solve. You are invited to try it as soon as you wish. You may find it hard for now, but by the end of Section 5, where its solution is given, it should not look difficult to you.
Alexander Zawaira, Gavin Hitchcock
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Diophantine equations

1986
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Quadratic Diophantine Equations

2004
34.1. We take a nondegenerate quadratic space \((V,\,{\varphi})\) of dimension \(\,n\,\) over a local or global field F in the sense of §21.1.
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Diophantine Equations

1995
Abstract Diophantus worked in Alexandria probably in the middle of the third century AD (some authors suggest early in the second century AD). His six or seven surviving books show that he had a highly developed understanding of many number theoretical problems.
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Diophantine equations

1992
Abstract A basic property of integers is that they can be expressed uniquely as a product of prime numbers. In this chapter we investigate other rings having a similar type of unique factorization property. As a means of motivating our investigation, let us begin by considering two number theoretic puzzles involving so-called Diophantine
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On a Diophantine equation involving primes

The Ramanujan journal, 2018
Yingchun Cai
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