Number Theory and Combinatorics

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 3 in Mathematical Olympiad Challenges, 2000, pp 197-249 from Springer

Abstract: Abstract 1. Let a,b,c,d,e,f be the six digits of the number, arranged in increasing order of their valaue. Choose for the first three digits f,c,aand for the last three digits e,d,b. Then f+c+a−e−d−b = (f−e)+(c−d)+(a−b) ≤ f−e≤9, since c−d and a−b are negative or zero. Also, e+d+b−c−a = (e−f)+(b−c)+(d−a)≤d−a≤9. Hence the number fcaedb satisfies the desired property.

Keywords: Number Theory; Nonnegative Integer; Residue Class; Great Common Divisor; Fibonacci Number (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1007/978-1-4612-2138-8_6

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