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We obtain an asymptotic formula for the average value of the divisor functionover the integers $n \le x$ in an arithmetic progression $n \equiv a \pmod q$,where $q=p^k$ for a prime $p\ge 3$ and a sufficiently large integer $k$. Inparticular, we break the classical barrier $q \le x^{2/3}$ for such formulas,and generalise a recent result of R.~Khan (2015), making it uniform in $k$.

Divisor problem in arithmetic progressions modulo a prime power