1
Part of 2009 Cuba MO
Problems(2)
routes in 4x7 grid
Source: 2008 Cuba Mo 1.1
8/27/2024
Juan and Pedro play alternately on the given grid. Each one in turn traces to routes different from the ones outlined above, that join with , moving only to the right and upwards on the grid lines. Juan starts playing. The one who traces a route that passes through or loses. Prove that one of them can win regardless of how the other plays.
https://cdn.artofproblemsolving.com/attachments/2/7/6a24ca9c4c1c710bd41e44bfcab3d3b61b6d4f.png
combinatorics
prime mod 30, 60, 90
Source: 2009 Cuba 2.1
8/27/2024
Show that when a prime number is divided by , the remainder is or a prime number. Shows that if it is divided by or the same thing does not happen.
number theoryremainderprime