Prove that discrete math the following statement (if true) or provide a counterexample (if false): For all n \geq 4, 2^n - 1 is not a prime number.

Jaya Legge 2021-08-10 Answered
Prove that discrete math the following statement (if true) or provide a counterexample (if false): For all n4,2n1 is not a prime number.
You can still ask an expert for help

Want to know more about Discrete math?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Caren
Answered 2021-08-11 Author has 96 answers

Counter example
n=5 Then 2n1=251=31
31 is a prime. So statement is false for n=5. As 54.

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-08-02
Suppose that A is the set of sophomores at your school and B is the set of students in discrete mathematics at your school. Express each of these sets in terms of A and B.
a) the set of sophomores taking discrete mathematics in your school
b) the set of sophomores at your school who are not taking discrete mathematics
c) the set of students at your school who either are sophomores or are taking discrete mathematics
Use these symbols:
asked 2021-07-28

Let A, B, and C be sets. Show that (AB)C=(AC)(BC)
image

asked 2020-11-09
Use proof by Contradiction to prove that the sum of an irrational number and a rational number is irrational.
asked 2021-08-15
How many elements are in the set { 0, { { 0 } }?
asked 2020-11-17
Make fractions out of the following information, reduce, if possible,
1 foot is divided into 12 inches. Make a fraction of the distance from 0 to a-d
0 to a. = ___
0 to b. = ___
0 to c. = ___
0 to d. = ___
asked 2022-05-21
Partitions of n where every element of the partition is different from 1 is p ( n ) p ( n 1 )
I am trying to prove that p(n| every element in the partition is different of 1 ) = p ( n ) p ( n 1 ), and I am quite lost... I have tried first giving a biyection between some sets, trying to draw an example in a Ferrers diagram and working on it... Nevertheless, I have not obtained significant results. Then, I have thought about generating functions; we know that the generating function of { p ( n ) } n N is i = 1 1 1 x i , so { p ( n 1 ) } n N will have i = 1 x 1 x i as generating function. So, what we have to prove is that i = 1 1 1 x i i = 1 x 1 x i = ( 1 -x). i = 1 1 1 x i is the generating function of p(n|every element in the partition is different of 1)... but i'm am not seeing why! Any help or hint will be appreciate it!
asked 2021-11-10
Suppose that A is the set of sophomores at your school and B is the set of students in discrete mathematics at your school. Express each of these sets in terms of A and B. a) the set of sophomores taking discrete mathematics in your school b) the set of sophomores at your school who are not taking discrete mathematics c) the set of students at your school who either are sophomores or are taking discrete mathematics

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question