Lower bound on product of binomial coefficients
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2015), pp. 21-26.

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We give a lower bound on a product of binomial coefficients, connected with primality proving or construction of high multiplicative order elements in finite fields.
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Roman B. Popovych. Lower bound on product of binomial coefficients. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2015), pp. 21-26. https://geodesic-test.mathdoc.fr/item/BASM_2015_2_a1/

[1] Agrawal M., Kayal N., Saxena N., “PRIMES is in $P$”, Ann. of Math., 160:2 (2004), 781–793 | DOI | MR | Zbl

[2] Ahmadi O., Shparlinski I. E., Voloch J. F., “Multiplicative order of Gauss periods”, Int. J. Number Theory, 6:4 (2010), 877–882 | DOI | MR | Zbl

[3] Bernstein D., “Proving primality in essentially quartic random time”, Math. Comp., 76:257 (2007), 391–403 | MR

[4] Berrizbeitia P., “Sharpening Primes is in $P$ for a large family of numbers”, Math. Comp., 74:252 (2005), 2043–2059 | DOI | MR | Zbl

[5] Burkhart J. F. et al., “Finite field elements of high order arising from modular curves”, Des. Codes Cryptogr., 51:3 (2009), 301–314 | DOI | MR | Zbl

[6] Cheng Q., “On the construction of finite field elements of large order”, Finite Fields Appl., 11:3 (2005), 358–366 | DOI | MR | Zbl

[7] Gao S., “Elements of provable high orders in finite fields”, Proc. Amer. Math. Soc., 107:6 (1999), 1615–1623 | DOI | MR

[8] Lidl R., Niederreiter H., Finite Fields, Cambridge University Press, 1997 | MR

[9] Mullen G. L., Panario D., Handbook of finite fields, CRC Press, 2013 | MR | Zbl

[10] Popovych R., “Elements of high order in finite fields of the form $F_q[x]/\Phi_r(x)$”, Finite Fields Appl., 18:4 (2012), 700–710 | DOI | MR | Zbl

[11] Popovych R., “Elements of high order in finite fields of the form $F_q[x]/(x^m-a)$”, Finite Fields Appl., 19:1 (2013), 86–92 | DOI | MR | Zbl

[12] Stanica P., “Good lower and upper bounds on binomial coefficients”, J. Inequal. Pure Appl. Math., 2:3 (2001), art. 30 | MR | Zbl

[13] Voloch J. F., “Elements of high order on finite fields from elliptic cures”, Bull. Austral. Math. Soc., 81:3 (2010), 425–429 | DOI | MR | Zbl