## Criterion for 3 to be eleventh power.(English)Zbl 0876.11002

The author gives a criterion for 3 to be an 11th power modulo a prime $$p$$ of the form $$p=x^2 +11y^2$$.
Reviewer: R.Mollin (Calgary)

### MSC:

 11A07 Congruences; primitive roots; residue systems 11D09 Quadratic and bilinear Diophantine equations 11N32 Primes represented by polynomials; other multiplicative structures of polynomial values 11R11 Quadratic extensions
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### References:

 [1] Alderson H. P.: On the septimic character of 2 and 3. Proc. Camb. Phil. Soc. 74 (1973), 421-433. · Zbl 0265.10003 [2] Ankeny N. C.: Criterion for rth power residuacity. Pacific J. Math. 10 (1960), 1115-1124. · Zbl 0113.26801 [3] Jacobi C. G. J.: De residuis cubicis commentatio numerosa. J. für Reine und Angew. Math. 2 (1827), 66-69. [4] Jakubec S.: Note on the Jacobi sum. Seminaire de theorie des nombres de Bordeaux to appear (1994). · Zbl 0816.11027 [5] Lehmer E.: The quintic character of 2 and 3. Duke Math. J. 18 (1951), 11-18. · Zbl 0045.02002 [6] Leonard P. A., Williams K. S.: The septic character of 2, 3, 5 and 7. Pacific J. Math. 52 (1974), 143-147. · Zbl 0265.10004 [7] Muskat J. B.: On the solvability of $$x^c \equiv e (\bmod p). Pacific J. Math. 14 (1964), 257-260.$$ · Zbl 0117.27701 [8] Parnami J. C., Agrawal M. K., Rajwade A.R.: Criterion for 2 to be l-th power. Acta Arith. 43 (1984), 361-364. · Zbl 0539.10006 [9] Williams K. S.: Explicit criteria for quintic residuacity. Math. Comp. 30 (1974), 1-6. · Zbl 0341.10004
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