Shichun Yang

Rank (linear algebra)Prime numberCombinatoricsDiscrete mathematicsAlgebraLink (knot theory)Ramanujan's sumSpace–time codeCentral binomial coefficientGaussian binomial coefficientInteger latticeExponential functionQuadratic functionNumber theoryPrime powerChebyshev functionGeneralizationSet (abstract data type)Prime (order theory)Lattice (group)Binomial seriesDiophantine equationCode (set theory)Open problemDiophantine quintupleConjectureBinomial (polynomial)Applied mathematicsRamanujan primeMathematicsLogarithmDiophantine setIntegerPrime number theoremFunction (mathematics)Upper and lower boundsDivisorProduct (mathematics)Binomial approximationDivisibility rule

11Publications

3H-index

17Citations

Publications 10

Newest

#1Shichun YangH-Index: 3

#2Florian LucaH-Index: 22

Last. Alain TogbéH-Index: 13

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#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.

#1Shichun YangH-Index: 3

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

For \(n\ge 1\), the nth Ramanujan prime is defined as the least positive integer \(R_{n}\) such that for all \(x\ge R_{n}\), the interval \((\frac{x}{2}, x]\) has at least n primes. Let \(p_{i}\) be the ith prime and \(R_{n}=p_{s}\). Sondow, Laishram, and other scholars gave a series of upper bounds of s. In this paper we establish several results giving estimates of upper and lower bounds of Ramanujan primes. Using these estimates, we discuss a conjecture on Ramanujan primes of Sondow–Nicholson...

#1Shichun YangH-Index: 3

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

Abstract Using the idea of Hajdu–Saradha–Tijdeman and the sharp estimate of the Chebyshev function θ ( x ) obtained by Dusart, we prove the P -integer conjecture, i.e. if k is a P -integer, then k ∈ { 2 , 4 , 6 , 12 , 18 , 30 } .

#1Shichun YangH-Index: 3

#2Alain TogbéH-Index: 13

Last. Wenquan Wu

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#1Bo HeH-Index: 7

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

Last. Shichun YangH-Index: 3

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Click on the link to view the abstract. Keywords: Exponential Diophantine equation, Terai conjecture, positive integer solution, linear forms in two logarithms, lower bound, primitive divisor Quaestiones Mathematicae 36(2013), 119–135

#1Shichun YangH-Index: 3

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

Last. Bo HeH-Index: 7

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Let a, b, c, d be given nonnegative integers with a,d⩾1. Using Chebyshevʼs inequalities for the function π(x) and some results concerning arithmetic progressions of prime numbers, we study the Diophantine equation ∏k=1n(ak2+bk+c)=dyl,gcd(a,b,c)=1,l⩾2, where ax2+bx+c is an irreducible quadratic polynomial. We provide a computable sharp upper bound to n. Using this bound, we entirely prove some conjectures due to Amdeberhan, Medina and Moll (2008) [1]. Moreover, we obtain all the positive integer ...

#1Bo HeH-Index: 7

#2Alain TogbéH-Index: 13

Last. Shichun YangH-Index: 3

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Let a,b,and cbe positive integers. We show that if (a,b) =(N^k-1,N) where N,k\geq 2 then there is at most one positive integer solution (x,y)to the exponential Diophantine equation |a^x-b^y|=c unless (N,k)=(2,2) Combining this with results of Bennett [3] and the first author [6], we stated all cases for which the equation |(N^k \pm 1)^x - N^y|=chas more than one positive integer solutions (x,y)

#1Shichun YangH-Index: 3

#2Bo HeH-Index: 7

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

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For all previous constructions of 2 x 2 lattice space-time codes with a positive diversity product, the rank r(2) was such that r(2) ≤ 4. An example of a 2 x 2 lattice space-time code of rank 5 with a positive diversity product was given by Xing and Li. In this paper, we give an example of a 2 x 2 lattice space-time code of rank 8 with a positive diversity product. This gives an answer to the open problem set by Xing and Li.

#1Shichun YangH-Index: 3

#2Bo HeH-Index: 7

Last. Alain TogbéH-Index: 13

view all 3 authors...

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