1988/01/01 by Andrew Granville, Michael Monagan · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #History and Theory of Mathematics #Analytic Number Theory Research #Algorithm #Annotation #Artificial intelligence #Computer science #Mathematics
paper · pdf · doi:10.1090/s0002-9947-1988-0927694-5
openalex publication_date 1988/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/19
We show that if the first case of Fermat’s Last Theorem is false for prime exponent <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> then <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p squared"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>p</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">p2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> divides <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="q Superscript p Baseline minus q"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>q</mml:mi> <mml:mi>p</mml:mi> </mml:msup> </mml:mrow> <mml:mo> − </mml:mo> <mml:mi>q</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">qp - q</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for all primes <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="q less-than-or-slanted-equals 8 q"> <mml:semantics> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo> ⩽ </mml:mo> <mml:mn>8</mml:mn> <mml:mi>q</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">q \leqslant 8q</mml:annotation> </mml:semantics> </mml:math> </inline-formula> . As a corollary we state the theorem of the title.