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We call a positive integer n amazing if there exist positive integers a, b, c such that the equality n = (b, c)(a, bc) + (c, a)(b, ca) + (a, b)(c, ab) holds. Prove that there exist 2011 consecutive positive integers which are amazing.

Note. By (m, n) we denote the greatest common divisor of positive integers m and n.

Slični zadaci

#NaslovOznakeRj.KvalitetaTežina
1353IMO Shortlist 1969 problem 230
1354IMO Shortlist 1969 problem 240
1355IMO Shortlist 1969 problem 250
2413MEMO 2007 ekipno problem 89
2445MEMO 2010 ekipno problem 82
2456MEMO 2011 ekipno problem 75