UM Mathletics[removed]Problem Set #3 K. Kopotun 1. Prove that there exists a positive integer n such that for every x ≥ 0 the inequality (x − 1)(x2005 − 2005xn+1 + 2005xn − 1) ≥ 0

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UM Mathletics[removed]Problem Set #5 K. Kopotun 1. Is it possible that both numbers 2n − 1 and 2n + 1 are prime for some n > 2? 2. Prove that the sum 1k + 2k + · · · + nk ,

Source URL: server.math.umanitoba.ca

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Source URL: www.math.ias.edu

• Computer science
• Applied mathematics
• Adversary model
• Competitive analysis
• K-server problem
• Randomized algorithm
• Algorithm
• List update problem
• Online algorithms
• Analysis of algorithms
• Theoretical computer science

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Source URL: people.csail.mit.edu

• Computer science
• Applied mathematics
• K-server problem
• Randomized algorithm
• Metrical task system
• SL
• Competitive analysis
• Adversary model
• David Shmoys
• Online algorithms
• Theoretical computer science
• Analysis of algorithms