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78:
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174:
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134:
102:
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501:(1823). "Recherches sur quelques objets d'analyse indéterminée et particulièrement sur le théorème de Fermat".
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537:"Voici ce que j'ai trouvé": Sophie Germain's grand plan to prove Fermat's Last Theorem
585:
542:
20:
536:
16:
On the divisibility of solutions to Fermat's Last
Theorem for prime exponent
457:
for every prime less than 100. The theorem and its application to primes
363:
Conversely, the first case of Fermat's Last
Theorem (the case in which
27:
is a statement about the divisibility of solutions to the equation
511:
Didot, Paris, 1827. Also appeared as Second Supplément (1825) to
463:
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can be found such that two conditions are satisfied:
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90:
33:
503:
MĂ©m. Acad. Roy. des
Sciences de l'Institut de France
551:. Cambridge: Cambridge University Press. pp.
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375:
351:
328:
296:
274:
251:
215:
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168:
148:
128:
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72:
429:for which even one auxiliary prime can be found.
567:. New York: Springer-Verlag. pp. 54–63.
8:
477:less than 100 were attributed to Germain by
515:, 2nd edn., Paris, 1808; also reprinted in
437:Germain identified such an auxiliary prime
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116:proved that at least one of the numbers
548:Three Lectures on Fermat's Last Theorem
490:
7:
565:13 Lectures on Fermat's Last Theorem
535:Laubenbacher R, Pengelley D (2007)
320:
317:
243:
240:
14:
329:{\displaystyle p^{\mathrm {th} }}
252:{\displaystyle p^{\mathrm {th} }}
73:{\displaystyle x^{p}+y^{p}=z^{p}}
513:Essai sur la théorie des nombres
1:
409:) must hold for every prime
613:
592:Theorems in number theory
25:Sophie Germain's theorem
471:
451:
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403:
377:
353:
330:
298:
276:
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217:
203:if an auxiliary prime
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170:
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98:
74:
597:Fermat's Last Theorem
479:Adrien-Marie Legendre
472:
452:
424:
404:
378:
354:
331:
299:
277:
259:powers differ by one
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218:
198:
196:{\displaystyle p^{2}}
176:must be divisible by
171:
151:
131:
99:
82:Fermat's Last Theorem
75:
461:
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387:
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31:
402:{\displaystyle xyz}
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70:
574:978-0-387-90432-0
470:{\displaystyle p}
450:{\displaystyle q}
422:{\displaystyle p}
376:{\displaystyle p}
352:{\displaystyle q}
297:{\displaystyle p}
275:{\displaystyle q}
216:{\displaystyle q}
169:{\displaystyle z}
149:{\displaystyle y}
129:{\displaystyle x}
97:{\displaystyle p}
604:
578:
556:
523:
510:
495:
476:
474:
473:
468:
456:
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383:does not divide
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380:
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304:is itself not a
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127:
108:Formal statement
103:
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100:
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56:
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43:
42:
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522:(1909), 97–128.
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365:
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234:
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228:
227:No two nonzero
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138:
137:
118:
117:
110:
86:
85:
60:
47:
34:
29:
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17:
12:
11:
5:
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271:
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145:
125:
114:Sophie Germain
112:Specifically,
109:
106:
93:
84:for odd prime
67:
63:
59:
54:
50:
46:
41:
37:
15:
13:
10:
9:
6:
4:
3:
2:
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550:
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538:
534:
533:
529:
521:
518:
517:Sphinx-Oedipe
514:
508:
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500:
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432:
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416:
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291:
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269:
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235:
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210:
188:
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163:
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123:
115:
107:
105:
91:
83:
65:
61:
57:
52:
48:
44:
39:
35:
26:
22:
21:number theory
564:
547:
519:
516:
512:
506:
502:
493:
436:
362:
111:
24:
18:
561:Ribenboim P
499:Legendre AM
586:Categories
543:Mordell LJ
530:References
481:in 1823.
563:(1979).
545:(1921).
433:History
571:
338:modulo
336:power
261:modulo
485:Notes
282:; and
569:ISBN
555:–31.
80:of
19:In
588::
553:27
505:.
156:,
136:,
104:.
23:,
577:.
520:4
509:.
507:6
465:p
445:q
417:p
397:z
394:y
391:x
371:p
359:.
347:q
321:h
318:t
313:p
292:p
270:q
244:h
241:t
236:p
211:q
189:2
185:p
164:z
144:y
124:x
92:p
66:p
62:z
58:=
53:p
49:y
45:+
40:p
36:x
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