Algebra and Analysis

Titu Andreescu and Răzvan Gelca
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Titu Andreescu: University of Nebraska, American Mathematics Competitions
Răzvan Gelca: University of Michigan, Department of Mathematics

Chapter Chapter 2 in Mathematical Olympiad Challenges, 2000, pp 151-195 from Springer

Abstract: Abstract 1. If the inequalities $$ a - {{b}^{2}} > \frac{1}{4},{\text{ }}b - {{c}^{2}} > \frac{1}{4},{\text{ }}c - {{d}^{2}} > \frac{1}{4},{\text{ }}d - {{a}^{2}} > \frac{1}{4} $$ hold simultaneously, then by adding them we obtain a+b+c+d−(a2+b2+c2+) > 1.

Keywords: Mathematic Review; Mathematical Competition; Mathematic Gazette; Bulgarian Mathematical; Abel Summation Formula (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1007/978-1-4612-2138-8_5

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