Question

Use Dirichlet’s theorem, which states there are infinitely many primes in every arithmetic progression ak + b where gcd(a, b) =1, to show that there are infinitely many primes that have a decimal expansion ending with a 1.

Short answer

Take a = 10 and b = 1 .

Step-by-step solution

Step 1:

Take a = 10 and b = 1.

Then Dirichlet’s theorem states that there are infinitely many primes of the form 10k + 1 , that is their decimal expansion ends in 1.