Question

Show that there is a composite integer in every arithmetic progression$ak+b,k=1,2,....$ where a and b are positive integers.

Short answer

$b\text{'}th$term is composite.

Step-by-step solution

Step 1

The $b\text{'}th$term of the given series is obtained by putting $k=bb\text{'}th$ term$=ab+b=\left(a+1\right)b$ which is composite (divisible$a+1$ by $b$).