#### Hall 123

#### Rough Numbers in Arithmetic Progressions

#### Kamalakshya Mahatab

##### IMSc

*We will give an asymptotic formula for number of numbers less*

than $x$ and prime factors are in the union of intervals, $(y_1, y_2]\cup

(y_3, y_4]\cdots \cup (y_l, \infty]$.

Done