Jumpy number base
Number Theory
Level
pending
First, convert decimal number 2^16-1 to binary number. Then, write this binary number down and consider it as a decimal number (NOT converting it back). All the following numbers are its factors except
1
11
1001
101
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1 solution
The number 2^16-1 is 65535, which converts to 1,111,111,111,111,111 (sixteen "1"s) in binary system. Considering that 1111 1,000,100,010,001=1,111,111,111,111,111 and 1111=11 101, this 16-digit number is divisible by 1,11 and 101. That leaves us the answer, which is 1001.