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UPDATE (10 April): You may assume that both
α1 and α2 are positive.
This is a classic riddle. References will be given on the solution page. Prove that given irrational α1 and α2 with 1/α1+1/α2=1, the sequences floor(i*α1) and floor(i*α2), for i=1,..., partition the naturals. (That is to say that every natural appears in exactly one of the sequences.) |
List of solvers:Hamidreza Bidar (1 April 20:34)Joseph DeVincentis (4 April 10:13) Oded Margalit (8 April 02:26) Adam Daire (11 April 00:50) Jaesong Lee (11 April 01:09) Djinn Lu (11 April 16:16) Albert Stadler (13 April 05:45) Sylvain Becker (13 April 21:59) Dan Dima (15 April 19:17) Ganesh Lakshminarayana (20 April 22:39) |
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The solution will be published at the end of the month.
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