Bo He

Hubei University

Rank (linear algebra)Pell's equationCombinatoricsDiscrete mathematicsAlgebraQuartic functionSpace–time codeClass (set theory)Exponential functionThue equationSquare numberGeneralizationSet (abstract data type)Prime (order theory)Diophantine equationDiophantine quintupleConjectureMathematicsDiophantine setIntegerUpper and lower boundsProduct (mathematics)Integer (computer science)

29Publications

7H-index

121Citations

Publications 26

Newest

#1Kouessi Norbert Adedji (National University of Benin)H-Index: 1

#2Bo HeH-Index: 7

Last. Alain Togbé (Purdue University)H-Index: 13

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Abstract The purpose of the present paper is to consider the extensibility of the Diophantine triple { a , b , c } , where a b c with b = 3 a , and to prove that such a set cannot be extended to an irregular Diophantine quadruple. We succeed in that for some families of c's (depending on a). As corollary, we prove that any Diophantine quadruple which contains the pair { a , 3 a } is regular. Finally in this paper, we will see that by considering the case b = 8 a we obviously obtain similar resul...

#1Volker ZieglerH-Index: 12

#2Alain TogbéH-Index: 13

Last. Bo HeH-Index: 7

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#1Bo He (Huda: Hubei University)H-Index: 7

#2Alain Togbé (Purdue University)H-Index: 13

Last. Volker Ziegler (University of Salzburg)H-Index: 12

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A set of mpositive integers \{a_1, a_2, \dots , a_m\}is called a Diophantine mtuple if a_i a_j + 1is a perfect square for all 1 \le i < j \le m In 2004 Dujella proved that there is no Diophantine sextuple and that there are at most finitely many Diophantine quintuples. In particular, a folklore conjecture concerning Diophantine mtuples states that no Diophantine quintuple exists at all. In this paper we prove this conjecture.

#1Bo He (Huda: Hubei University)H-Index: 7

#2Ákos Pintér (MTA: Hungarian Academy of Sciences)H-Index: 13

Last. Shichun YangH-Index: 3

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Abstract Dujella and Pethő, generalizing a result of Baker and Davenport, proved that the set { 1 , 3 } cannot be extended to a Diophantine quintuple. As a consequence of our main result, we show that the Diophantine pair { 1 , b } is regular if b − 1 is a prime power.

#1Bo HeH-Index: 7

#2Keli PuH-Index: 1

Last. Alain TogbéH-Index: 13

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#2Bo He (Huda: Hubei University)H-Index: 7

Last. Alain Togbé (Purdue University)H-Index: 13

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In this paper, we consider the \(D(\pm k)\)-triple \(\{k\mp 1,k, 4k\mp 1\}\) and we prove that, if k is not a perfect square then: (1) There is no d such that \(\{k-1,k, 4k-1, d\}\) is a D(k)-quadruple; (2) If \(\{k,k+1,4k+1,d \}\) is a \(D(-k)\)-quadruple, then \(d=1\). This extends a work done by Fujita [13].

#1Bo He (Huda: Hubei University)H-Index: 7

#2Florian Luca (University of the Witwatersrand)H-Index: 22

Last. Alain Togbé (Purdue University)H-Index: 13

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#1Bo HeH-Index: 7

#2Ákos Pintér (MTA: Hungarian Academy of Sciences)H-Index: 13

Last. Alain Togbé (Purdue University North Central)H-Index: 13

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#1Alain TogbéH-Index: 13

#2Ákos PintérH-Index: 13

Last. Nóra VargaH-Index: 6

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#1Bo HeH-Index: 7

#2István PinkH-Index: 9

Last. Alain Togbé (Purdue University North Central)H-Index: 13

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