Hey Guys,
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
Hey Guys,
This is what I originally figured out:
log(2)^1000000*6.972593, know that low log(2) ~ 0.3010
therefore 1000000*.3010 ~ 300000 * 6.97 = 2.091*10^6
However I think that would be considered multiplying it out, I just couldn't figure out any other way.
Aidan I appreciate the explanation, just one question log(10) = 1 correct? assuming its base 10 and logb(b) = 1.
It doesn't matter what base you use, as long as you use the same base for log(2) and log(10). You could choose base 2 or base 10, or base e -- the ratio will remain constant.
In fact, unless a base is specifically given, you should always assume the base is e in a mathematical context.