2020•Mathematics MagazineRequires access
Why Does a Prime p Divide a Fermat Number?
Zafer Selçuk Aygin, Kenneth S. Williams
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Abstract
SummaryA prime dividing a composite Fermat number is called a Fermat prime divisor. Such a prime p must be congruent to 1 modulo 4, and so, by the Fermat–Girard theorem, there exists integers R and S such that p = R2 + S2. We derive a necessary and sufficient condition for p to be a Fermat prime divisor in terms of the integers R and S.