Number Theory proof of the day--11/19

[Steven G]

Show that there are no arithmetic progressions, a, a+1b, a+2b, ...,that contain solely prime numbers.

 

[lev888]

Show that there are no arithmetic progressions, a, a+1b, a+2b, ...,that contain solely prime numbers.

Spoiler

a+ab can't be a prime.

 

[Steven G]

Now show that a, a+1b, a+2b, .... must contain infinitely many composite numbers.

 

[lev888]

Now show that a, a+1b, a+2b, .... must contain infinitely many composite numbers.

Spoiler

a+(a^k)b