Min Tang
Anhui Normal University
Perfect numberOrder (group theory)CombinatoricsDiscrete mathematicsBasis (linear algebra)AlgebraCollatz conjectureMathematical analysisSquare (algebra)Existential quantificationSet (abstract data type)Prime (order theory)Pure mathematicsDiophantine equationCoprime integersChenRepresentation (systemics)SigmaBasis (universal algebra)ConjectureAlmost perfect numberCalculusMathematicsBounded functionIntegerPartition (number theory)If and only ifRepresentation (mathematics)Function (mathematics)Integer sequenceMonotonic functionErdos–Gyárfás conjectureDivisorReal number
12Publications
5H-index
65Citations
Publications 9
#1Dengrong Ling (Anhui Normal University)H-Index: 1
#2Min Tang (Anhui Normal University)H-Index: 5
We study a question on minimal asymptotic bases asked by Nathanson [‘Minimal bases and powers of 2’, Acta Arith. 49 (1988), 525–532].
#1Min Tang (Anhui Normal University)H-Index: 5
#1Min Tang (Anhui Normal University)H-Index: 5
#2Min Feng (Anhui Normal University)H-Index: 1
For a positive integer $$n$$, let $$\sigma(n)$$ denote the sum of the positive divisors of $$n$$. Let $$d$$ be a proper divisor of $$n$$, we call $$n$$ a deficient-perfect number if $$\sigma(n) = 2n - d$$. In this paper, we show that there is no odd deficient-perfect number with three distinct prime divisors. DOI: 10.1017/S0004972714000082
#1Min Tang (Anhui Normal University)H-Index: 5
#2Zhi-Juan Yang (Anhui Normal University)H-Index: 2
Let a, b, cbe relatively prime positive integers such that {a}^{2} + {b}^{2} = {c}^{2} . In 1956, Jeśmanowicz conjectured that for any positive integer n, the only solution of \mathop{(an)}\nolimits ^{x} + \mathop{(bn)}\nolimits ^{y} = \mathop{(cn)}\nolimits ^{z} in positive integers is (x, y, z)= (2, 2, 2). In this paper, we consider Jeśmanowicz’ conjecture for Pythagorean triples (a, b, c)if a= c- 2and cis a Fermat prime. For example, we show that Jeśmanowicz’ conjectur...
#1Zhi-Juan Yang (Anhui Normal University)H-Index: 2
#2Min Tang (Anhui Normal University)H-Index: 5
Let a,b,cbe relatively prime positive integers such that a^{2}+b^{2}=c^{2}.In 1956, Je\'{s}manowicz conjectured that for any given positive integer nthe only solution of (an)^{x}+(bn)^{y}=(cn)^{z}in positive integers is (x,y,z)=(2,2,2) In this paper, we show that (8n)^{x}+(15n)^{y}=(17n)^{z}has no solution other than (x,y,z)=(2,2,2)in positive integers. DOI: 10.1017/S000497271100342X
#1Min Tang (Anhui Normal University)H-Index: 5
Let Abe an asymptotic basis of integers with prescribed representation function, then how dense Acan be. In this paper, we prove that there exist a real number c>0and a asymptotic basis Awith prescribed representation function such that A(-x,x)\geq c\sqrt{x}for infinitely many positive integers x
#1Min Tang (Anhui Normal University)H-Index: 5
Let σ A ( n )=∣{( a , a′ )∈ A 2 : a + a′ = n }∣, where and A is a subset of . Erdos and Turan conjectured that, for any basis A of , σ A ( n ) is unbounded. In 1990, Ruzsa constructed a basis for which σ A ( n ) is bounded in the square mean. In this paper, based on Ruzsa’s method, we show that there exists a basis A of satisfying for large enough N .
#1Min Tang (Anhui Normal University)H-Index: 5
#1Yong-Gao Chen (Nanjing Normal University)H-Index: 10
#2András Sárközy (Alfréd Rényi Institute of Mathematics)H-Index: 29
Last. Min Tang (Anhui Normal University)H-Index: 5
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If A is a set of positive integers, let R1 (n) be the number of solutions of a + a′ = n, a. a′ ∈ A, and let R2(n) and R3(n) denote the number of solutions with the additional restrictions a < a′, and a ≤ a′ respectively. The monotonicity properties of the three functions R1(n), R2(n), and R3(n) are studied and compared.