Note on the congruences $2^{p-1}\equiv 1\hspace{4.44443pt}(\@mod \; p^2)$, $3^{p-1}\equiv 1\hspace{4.44443pt}(\@mod \; p^2)$, $5^{p-1}\equiv 1\hspace{4.44443pt}(\@mod \; p^2)$

Stanislav Jakubec

Tribonacci modulo $2^{t}$ and $11^{t}$

Jiří Klaška (2008)

Mathematica Bohemica

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Our previous research was devoted to the problem of determining the primitive periods of the sequences ${(G_{n} mod p^{t})}_{n = 1}^{\infty}$ where ${(G_{n})}_{n = 1}^{\infty}$ is a Tribonacci sequence defined by an arbitrary triple of integers. The solution to this problem was found for the case of powers of an arbitrary prime $p \neq 2, 11$ . In this paper, which could be seen as a completion of our preceding investigation, we find solution for the case of singular primes $p = 2, 11$ .

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Displaying similar documents to “Note on the congruences 2 p - 1 ≡ 1 ( mod p 2 ) , 3 p - 1 ≡ 1 ( mod p 2 ) , 5 p - 1 ≡ 1 ( mod p 2 ) ”

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Displaying similar documents to “Note on the congruences $2^{p - 1} \equiv 1 (mod p^{2})$ , $3^{p - 1} \equiv 1 (mod p^{2})$ , $5^{p - 1} \equiv 1 (mod p^{2})$ ”

Tribonacci modulo $2^{t}$ and $11^{t}$