Sophie's diary (Q2886999)

The book under review is a work of fiction inspired by the French mathematician Sophie Germain (April 1, 1776 -- June 27, 1831). The author develops a fictional character inspired by Sophie Germain. This volume contains mathematical details, intertwined with historically-accurate accounts of the social chaos that reigned in Paris between 1789 and 1794. A particular interest is given to Sophie Germain's contribution to the proof of Fermat's Last Theorem. One of her main contributions in this field is the following.NEWLINENEWLINELet \(p\) be an odd prime. Assume there exists an auxiliary prime \(P = 2Np + 1\) such that the following properties hold true:NEWLINENEWLINE(i) if \(xp + yp + zp = 0\) (mod \(P\)) then \(P\) divides \(xyz\), andNEWLINENEWLINE(ii) \( p\) is not a \(p\)th power residue (mod \(P\)).NEWLINENEWLINEThen Fermat's Last Theorem holds true for the exponent \(p\), provided that \(p\) does not divide any of \(x\), \(y\), or \(z\).NEWLINENEWLINESophie Germain also made important contributions to mathematical physics and number theory. These contributions, as well as other interesting facts, are developed in the present volume.