22 mod 2=4 mod 2=0
23 mod 3=8 mod 3=2
24 mod 4=16 mod 4=0
25 mod 5=32 mod 5=2
26 mod 6=64 mod 6=4
27 mod 7=128 mod 7=2
28 mod 8=256 mod 8=0
29 mod 9=512 mod 9=8
210 mod 10=1024 mod 10=4
Therefore, the sequence 2n mod n starts 0, 0, 2, 0, 2, 4, 2, 0, 8, 4, ... Notice that all of the terms so far are either 0 or a power of 2.
1. What is the smallest positive integer n such that 2n mod n is neither 0 nor a power of 2?
2. What is the smallest positive integer n such that 2n mod n is odd?
3. Is there a positive integer n such that 2n mod n=1?
4. Which positive integer from 2 to 10 is the last to appear as 2n mod n for the first time?
Parts 1, 2, and 4 (and probably 3)
