Geodesic
Euler's Criterion for Quintic Nonresidues
Canadian journal of mathematics, Tome 37 (1985) no. 5, pp. 1008-1024

Voir la notice de l'article provenant de la source Cambridge University Press

Let e be an integer ≧ 2, and p a prime = 1 (mod e). Euler's criterion states that for D ∊ Z, (1.1) if and only if D is an e-th power residue (mod p). If D is not an e-th power (mod p), one has (1.2) for some e-th root α(≠1) of unity (mod p). Sometimes expressions for roots of unity (mod p) can be given in terms of quadratic partitions of p. For example, (1.3) are the four distinct fourth roots of unity (mod p) for a prime p ≡ 1 (mod 4) in terms of a solution (a, b) of the diophantine system (a, b unique), whereas for p ≡ 1 (mod 3), a solution (L, M) of the system gives (1.4) as the three distinct cuberoots of unity (mod p). 
Katre, S. A.; Rajwade, A. R. Euler's Criterion for Quintic Nonresidues. Canadian journal of mathematics, Tome 37 (1985) no. 5, pp. 1008-1024. doi: 10.4153/CJM-1985-054-2
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