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(1)

Épreuve de setion européenne

The Oxford Murders

TheOxfordMurdersisaSpanish-British-Frenhlm,direted

in 2008byAlexde laIglesia,adapted from thenovelbytheAr-

gentinemathematiianandwriterGuillermoMartínez.

Hereisthebeginningoftheplot: atOxfordUniversity,Martin

isanAmerianstudentwhowantsProfessorArthurSeldomashis

thesis supervisor. He idolises Seldom and has learned allabout

him. Inapublileture,Seldomdeniesthepossibilityofabsolute

truth. Hopingtoimpresshis idol,Martindisputesthis, asserting

his faith in the absolute truth of mathematis: I believein the

numberPi,intheGoldenRatio,intheFibonaisequene. Con-

sequently,ifwedisovertheseretsigniationofnumbers,we'll

unveil the hidden sense of reality. Finally, they work together

to tryandstopapotentialseriesofmurdersseeminglylinkedby

mathematialsymbols...

The haraters debate several mathematial, physial and

philosophialoneptssuh aslogialseries, Heisenberg'sPrini-

pleofUnertainty,Gödel'sTheorem,thepossibilityoftheperfet

rime,Fermat's LastTheorem,theButteryeet,et.

TheOxfordmurders

movieposter

Pierre deFermat

Bormat'sLastTheorem thatissolvedinthemovieislearly

areferenetoFermat'sLastTheorem.

Fermat's LastTheorem statesthatno three nonzeropositive

integers

a

,

b

,and

c

ansatisfytheequation

a n + b n = c n

forany integer

n

greaterthantwo.

This theoremwasrstonjeturedbytheFrenh mathemati-

ianPierre de Fermat in 1637. Helaimed he had a proof that

was toolargeto tinthemargin...Butthistheoremwaswidely

onsideredtobeoneofthemostdiultproblemsinthelast300

years. It wasonlysolvedin 1995 bythe English mathematiian

AndrewWilesatPrineton (USA).

Adaptedfrom Wikipedia

Questions

1. Quoteafewmathematialideasandnumbersinvolvedinthelm.

2. Explain whatFermat'sLastTheorem is. DidFermat atuallyproveit?

3. Fermat's LastTheoremappliesfor any integer

n

greaterthan2. Explain whyit'spossible to ndthree values

a

,

b

and

c

suhthat

a 2 + b 2 = c 2

. Giveafewexamples.

4. (a) Explainwhy,ifthereexistthreenaturalnumbers

a

,

b

,

c

,suhthat

a 15 + b 15 = c 15

,it's easytondsuhasolutionforexponents5and3.

(b) Consideranon-primenumber

n

,andassumethatthereexistthreenaturalnumbers

a

,

b

,

c

suh that

a n + b n = c n

. Provethat therearealsosolutionsforanyexponentthat isadivisorof

n

.

Références

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