1.
Use the
next_prime() command to construct two different 8-digit prime numbers and save them in variables named a and b.Exercises 2.8 Sage Exercises
These exercises are about investigating basic properties of the integers, something we will frequently do when investigating groups. Sage worksheets have extensive capabilities for making new cells with carefully formatted text, include support for LaTeX syntax to express mathematics. So when a question asks for explanation or commentary, make a new cell and communicate clearly with your audience.
2.
3.
Verify that
4.
Find two integers that make a βlinear combinationβ of your two primes equal to
5.
Determine a factorization into powers of primes for
6.
Write a compute cell that defines the same value of
c again, and then defines a candidate divisor of c named d. The third line of the cell should return True if and only if d is a divisor of c. Illustrate the use of your cell by testing your code with 
