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The Diophantine Equation 8x + p y = z 2
  • Lan Qi, X. Li
  • Mathematics, Medicine
  • TheScientificWorldJournal
  • 14 January 2015
TLDR
Using certain results of exponential Diophantine equations, we prove that (i) if p ≡ ±3(mod  8), then the equation 8x + p y = z 2 has no positive integer solutions (x, y, z). Expand
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The Exponential Diophantine Equation 2x + b y = c z
  • Yahui Yu, X. Li
  • Mathematics, Medicine
  • TheScientificWorldJournal
  • 18 May 2014
Let b and c be fixed coprime odd positive integers with min{b, c} > 1. In this paper, a classification of all positive integer solutions (x, y, z) of the equation 2x + b y = c z is given. Further, byExpand
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AMPK Inhibition Suppresses the Malignant Phenotype of Pancreatic Cancer Cells in Part by Attenuating Aerobic Glycolysis
Pancreatic cancer is a highly aggressive tumor characterized by enhanced aerobic glycolysis. AMP-activated protein kinase (AMPK), which is identified as a well-known regulator of glycolysis, plays anExpand
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Association between Vaginal Micro-environment Disorder and Cervical Intraepithelial Neoplasia in a Community Based Population in China
There are other factors that contribute to cervical carcinogenesis except HPV infection. This study aimed to investigate the association between vaginal micro-environment factors, including H2O2,Expand
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The Exponential Diophantine Equation ${(4{m}^{2}+1)}^{x}+{({5m}^{2}-1)}^{y}={(3m)}^{z}$
Let m be a positive integer. In this paper, using some properties of exponential diophantine equations and some results on the existence of primitive divisors of Lucas numbers, we prove that if and ,Expand
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On the Smarandache-Pascal derived sequences and some of their conjectures
For any sequence {bn}, the Smarandache-Pascal derived sequence {Tn} of {bn} is defined as T1=b1, T2=b1+b2, T3=b1+2b2+b3, generally, Tn+1=∑k=0n(nk)⋅bk+1 for all n≥2, where (nk)=n!k!(n−k)! is theExpand
  • 1
On the Hybrid Power Mean Involving the Two-Term Exponential Sums and Polynomial Character Sums
The main purpose of this paper is using the analytic method and the properties of trigonometric sums and character sums to study the computational problem of one kind hybrid power mean involvingExpand
General solution for complete plane strain problem of a nonhomogeneous body with a doubly‐periodic set of inlays
  • X. Li
  • Mathematics
  • 1 September 2006
In this paper, we study the complete plane strain problem of a nonhomogeneous body with a doubly-periodic set of cylindrical inlay by using the complex potential method, which is one of the mostExpand
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The upper bound estimate of the number of integer points on elliptic curves y2=x3+p2rx
Let p be a fixed prime and r be a fixed positive integer. Further let N(p2r) denote the number of pairs of integer points (x,±y) on the elliptic curve E:y2=x3+p2rx with y>0. Using some properties ofExpand
Tagging Talkers in a Noisy, Reverberant Large-aperture Microphone-Array Environment
The problem of associating source tags for conversational speech segments from an unknown number of initially unenrolled talkers who are moving about the focal volume of a large-aperture microphoneExpand
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