Dat Do edited beginproblem_Alices_.tex  about 10 years ago

Commit id: 65355ca003e80971ad2ad20b0b5e20f769262832

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\\Computing the first letter, $11^{37} (mod\: 77)$  \\$11*11^{36} (mod\: 77)$  \\$11*121^{18} (mod\: 77)$  \\$11*(44^2)^{9} (mod\: 77)$ \\$11*11^9 (mod\: 77)$  \\$11*11*11^8 (mod\: 77)$  \\$11*11*121^4 (mod\: 77)$  \\$11*11*(44^2)^2 (mod\: 77)$  \\$11*11*11^2 (mod\: 77)$  \\$11*11*44 (mod\: 77)$  \\$121*44 (mod\: 77)$  \\$44*44 (mod\: 77)$  \\$=11 (mod\: 77)$  \\The first letter is $11$ or G.