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For a special case (when $a=\pm 1$) see

About irreducible trinomialsAbout irreducible trinomials

Testing irreducibilty over small moduli (obviously, if your polynomial is irreducible modulo $p,$ it is irreducible), is described in detail in this paper of Richard Brent's.

For a special case (when $a=\pm 1$) see

About irreducible trinomials

Testing irreducibilty over small moduli (obviously, if your polynomial is irreducible modulo $p,$ it is irreducible), is described in detail in this paper of Richard Brent's.

For a special case (when $a=\pm 1$) see

About irreducible trinomials

Testing irreducibilty over small moduli (obviously, if your polynomial is irreducible modulo $p,$ it is irreducible), is described in detail in this paper of Richard Brent's.

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Igor Rivin
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For a special case (when $a=\pm 1$) see

About irreducible trinomials

Testing irreducibilty over small moduli (obviously, if your polynomial is irreducible modulo $p,$ it is irreducible), is described in detail in this paper of Richard Brent's.