On the Largest Prime Factor of Integers in Short Intervals
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The author sharpens a result of Jia and Liu (2000), showing that for sufficiently large $x$, the interval $[x, x+x^{\frac{1}{2}+\varepsilon}]$ contains an integer with a prime factor larger than $x^{\frac{51}{53}-\varepsilon}$. This gives a solution with $\gamma = \frac{2}{53}$ to the Exercise 5.1 in Harman's book.