This is my first post and I imagine there will be a few more judging by how many questions I'm stumped on. Here the first question:
some of you many recognize this value...
2^6972593 - 1
A) Without multiplying it out, determine how many digits are needed to write out this number using base-10
B) Use the factor theorem to show that if 2^p - 1, where p does not equal 3, is a prime number , then p is neither divisible by 4 or divisible by 3. Alternatively , prove that if p is divisible by 4 or 3, then 2^p - 1 is divisible by some number other than +/- itself or +/- .
Thanks for the help