Another Note on the Greatest Prime Factors of Fermat Numbers

@article{Grytczuk2001AnotherNO,
  title={Another Note on the Greatest Prime Factors of Fermat Numbers},
  author={A. Grytczuk and M. W{\'o}jtowicz and F. Luca},
  journal={Southeast Asian Bulletin of Mathematics},
  year={2001},
  volume={25},
  pages={111-115}
}
For every positive integer k > 1, let P(k) be the largest prime divisor of k. In this note, we show that if Fm = 22m + 1 is the m‘th Fermat number, then P(Fm) ≥ 2m+2(4m + 9) + 1 for all m ≥ 4. We also give a lower bound of a similar type for P(Fa,m), where Fa,m = a2m + 1 whenever a is even and m ≥ a18. 
About Diophantine Equations, an Analytic Approach
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References

On the large sieve