Determine all possible integers n less than 10
100 that simultaneously satisfy these conditions:
- n divides 2n
- n - 1 divides 2n - 1
- n - 2 divides 2n - 2
Note: As an extra challenge, determine a semi-analytic (simple calculator + p&p) solution to this problem.
**** Adapted from a problem appearing at a William Lowell Putnam Mathematics Competition
2^(2^(2^3))=2^(2^8)=2^256=
115792089237316195423570985008687907853269984665640564039457584007913129639936<10^100, so there is another solution. The solutions are 4, 16, 65536, and 115792089237316195423570985008687907853269984665640564039457584007913129639936.
2^(2^(2^0))=2^(2^1)=2^2=4
2^(2^(2^1))=2^(2^2)=2^4=16
2^(2^(2^2))=2^(2^4)=2^16=65536
2^(2^(2^3))=2^(2^8)=2^256=115792089237316195423570985008687907853269984665640564039457584007913129639936
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Posted by Math Man
on 2023-06-19 12:58:25 |
There is another solution.
