SOLUTION: 15th august is a monday.show that after 2^n days there will not be monday.so, which are possible days?

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Question 476021: 15th august is a monday.show that after 2^n days there will not be monday.so, which are possible days?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Already solved...the day that occurs 2^n days after a Monday will be a Monday only if 2^n is a multiple of 7 (which is impossible). The residues of 2^n modulo 7 are 1, 2, 4 (8 is 1 mod 7, so the pattern repeats), so the only possible days are Tuesday (1 day after Monday), Wednesday (2 days after Monday) and Friday (4 days after Monday).