Perfect Polynomials Over GF(q)
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1975-03Author
O'Connell, James R., Jr.
Beard, Jacob T. B., Jr.
West, Karen I.
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**Please note that the full text is embargoed** ABSTRACT: A monic polynomial [see pdf for notation] is called perfect over GF(q) if and only if the sum [see pdf for notation] of the distinct monic divisors in GF[q,x] of A(x) equals A(x). Principal results characterize all perfect polynomials over GF(p) which split in GF[p,x]. Related results lead to conjectured analogs of the classical problem on the existence of odd perfect numbers.