Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Problem 4. Let n be any positive integer. Prove that there exists a positive integer k (depending on n) such that the following list of n consecutive integers: k, k + 1, k+n-1 contains no prime number at all. Hint. Use the factorial (but k =n! is NOT the correct answer, start from this and try to see what are missing). You also need the 2-out-of-3 property of division.

Problem 4. Let n be any positive integer. Prove that there exists a positive integer k (depending on n) such that the following list of n consecutive integers: k, k + 1, k+n-1 contains no prime number at all. Hint. Use the factorial (but k =n! is NOT the correct answer, start from this and try to see what are missing). You also need the 2-out-of-3 property of division.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
Problem 4. Let n be any positive integer. Prove that there exists a positive integer k (depending on n) such that the following list of n consecutive integers: k, k + 1, ·, k + n - 1 contains no prime number at all. = Hint. Use the factorial (but k n! is NOT the correct answer, start from this and try to see what are missing). You also need the 2-out-of-3 property of division.
Transcribed Image Text:Problem 4. Let n be any positive integer. Prove that there exists a positive integer k (depending on n) such that the following list of n consecutive integers: k, k + 1, ·, k + n - 1 contains no prime number at all. = Hint. Use the factorial (but k n! is NOT the correct answer, start from this and try to see what are missing). You also need the 2-out-of-3 property of division.
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS