Problems & Puzzles:
m +/-2^k+/-1 integers.
On May 26, 2018 Arkadiusz Wesolowski wrote:
I observed in 2017 that:
1) 247371098958 is a nonnegative even number m such that for all k >= 1
the numbers m + 2^k + 1 and m + 2^k - 1 are composite.
2) 444813635232 is a nonnegative even number m such that for all k >= 1
the absolute values of the numbers m - 2^k + 1 and m - 2^k - 1 are
Q1. Can you find "smaller" solutions?
Q2. Are there any nonnegative even numbers that cannot be written in the
form ± 2^k ± 1 ± p where p is a prime number, k∈N and any choice of
signs may be made?