Geodesic
A new solution to the equation \(\tau(p)\equiv 0\pmod p\)
Journal of integer sequences, Tome 13 (2010) no. 7
The known solutions to the equation $\tau (p) \equiv 0 (mod p)$ were $p = 2, 3, 5$, 7, and 2411. Here we present our method to compute the next solution, which is $p = 7758337633$. There are no other solutions up to $10^{10}$.
Keywords: tau function, non-ordinary primes, eichler-Selberg trace formula, Hurwitz sums, Catalan triangle, Ramanujan function, computation record 
@article{JIS_2010__13_7_a7,
     author = {Lygeros,  Nik and Rozier,  Olivier},
     title = {A new solution to the equation \(\tau(p)\equiv 0\pmod p\)},
     journal = {Journal of integer sequences},
     year = {2010},
     volume = {13},
     number = {7},
     zbl = {1216.11055},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2010__13_7_a7/}
}
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Lygeros,  Nik; Rozier,  Olivier. A new solution to the equation \(\tau(p)\equiv 0\pmod p\). Journal of integer sequences, Tome 13 (2010) no. 7. http://geodesic.mathdoc.fr/item/JIS_2010__13_7_a7/