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Research Article

On two conjectures of irreducible polynomials

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Pages 4879-4884 | Received 08 May 2023, Accepted 21 May 2023, Published online: 16 Jun 2023

References

  • Barbeau, E. J. (2003). Polynomials, Problem Books in Mathematics. New York: Springer-Verlag.
  • Bonciocat, N. C. (2015). Schönemann-Eisenstein-Dumas-type irreducibility conditions that use arbitrarily many prime numbers. Commun. Algebra 43(8):3102–3122. DOI: 10.1080/00927872.2014.910800.
  • Bonciocat, A. I., Bonciocat, N. C. (2006). Some classes of irreducible polynomials. Acta Arith. 123:349–360. DOI: 10.4064/aa123-4-4.
  • Bonciocat, A. I., Bonciocat, N. C. (2009). On the irreducibility of polynomials with leading coefficient divisible by a large prime power. Amer. Math. Monthly 116(8):743–745. DOI: 10.4169/193009709X460895.
  • Bonciocat, N. C., Bugeaud, Y., Cipu, M., Mignotte, M. (2013). Irreducibility criteria for sums of two relatively prime polynomials. Int. J. Number Theory 9(6):1529–1539. DOI: 10.1142/S1793042113500413.
  • onway, J. B. (1978). Functions of One Complex Variable. New York: Springer-Verlag.
  • Dumas, G. (1906). Sur quelques cas d’irreductibilité des polynômes á coefficients rationnels. Journal de Math. Pure et Appl. 2:191–258.
  • Filaseta, M. (1995). The irreducibility of all but finitely many Bessel polynomials. Acta Math. 174:383–397. DOI: 10.1007/BF02392470.
  • Filaseta, M., Finch, C., Leidy, J. R. (2005). T.N. Shorey’s influence in the theory of irreducible polynomials. In: Saradha, N., ed. Diophantine Equations. New Delhi: Narosa Publishing House, pp. 77–102.
  • Filaseta, M., Kidd, T., Trifonov, O. (2012). Laguerre polynomials with Galois group Am for each m. J. Number Theory 132:776–805. DOI: 10.1016/j.jnt.2011.09.012.
  • Filaseta, M., Williams, Jr. R. L. (2003). On the Irreducibility of a certain class of Laguerre polynomials. J. Number Theory 100:229–250. DOI: 10.1016/S0022-314X(02)00129-4.
  • Filaseta, M., Lam, T. Y. (2002). On the irreducibility of the generalized Laguerre polynomials. Acta Arith. 105: 177–182. DOI: 10.4064/aa105-2-4.
  • Filaseta, M., Moy, R. (2018). On the Galois group over Q of a truncated binomial expansion. Colloq. Math. 154(2):295–308.
  • Filaseta, M., Trifonov, O. (2002). The irreducibility of the Bessel polynomials. J. Reine Angew. Math. 550:125–140.
  • Gao, S. (2001). Absolute irreducibility of polynomials via Newton polytopes. J. Algebra 237(2):501–520. DOI: 10.1006/jabr.2000.8586.
  • Hajir, F. (1995). Some An-extensions obtained from generalized Laguerre polynomials. J. Number Theory 50: 206–212. DOI: 10.1006/jnth.1995.1015.
  • Harrington, J. (2012). On the factorization of the trinomials xn+cxn−1+d. Int. J. Number Theory 8(6):1513–1518.
  • Jonassen, A. T. (1967). On the irreducibility of the trinomials xn±xm±4. Math. Scand. 21:177–189.
  • Koley, B., Reddy, A. S. (2022). An irreducible class of polynomials over integers. J. Ramanujan Math. Soc. 37(4): 319–330.
  • Koley, B., Reddy, A. S. An irreducibility criterion of polynomials over integers, Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie. (To appear.)
  • Panitopol, L., Stefänescu, D. (1985). Some criteria for irreducibility of polynomials. Bull. Math. Soc. Sci. Math. R. S. Roumanie (N. S.) 29:69–74.
  • Sell, E. A. (2004). On a certain family of generalized Laguerre polynomials. J. Number Theory 107:266–281. DOI: 10.1016/j.jnt.2004.03.004.
  • Singh, J., Kumar, S. (2021). A new class of irreducible polynomials. Commun. Algebra 49(6):2722–2727. DOI: 10.1080/00927872.2021.1881789.
  • Sawin, W., Shusterman, M., Stoll, M. (2020). Irreducibility of polynomials with a large gap. Acta Arith. 192:111–139. DOI: 10.4064/aa180526-12-6.
  • Weisner, L. (1934). Criteria for the irreducibility of polynomials. Bull. Amer. Math. Soc. 40:864–870. DOI: 10.1090/S0002-9904-1934-05989-5.

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