From: Skouteris Dimitris (dimitris(@)impact.dyn.unipg.it)
Date: Πεμ 11 Απρ 2002 - 18:22:41 EEST

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Kalhmera se olous. Prin dwsw th lush, ta onomata autwn pou to vrhkan:

Voula Alexiadou
Vaggelis Kapoulas

Apanthseis hmiteleis/esfalmenes esteilan epishs oi :

Christos Papadopoulos
Korbas
sugaros
Panagiotis Papadakis

OK, arxizoume. Parte va0ia anasa. As piasoume ena ena ta stoixeia tou dialogou :

Par' olo pou o G 3erei to ginomeno, den mporei na upologisei tous ari0mous. Auto shmainei oti to ginomeno tou epidexetai panw apo mia luseis, opws as poume to 28 = 2 x 14 = 4 x 7. Ena tetoio ginomeno as to poume 'asafes'.

3erontas mono to a0roisma, o A einai se 0esh na gnwrizei oti o G den tous 3erei, oti dhladh to ginomeno einai asafes. Auto shmainei oti *ka0e pi0anh lush* pou antistoixei sto a0roisma tou A exei asafes ginomeno.

Auto periorizei kata polu ta pi0ana a0roismata. To a0roisma den mporei na einai artio, afou ka0e artios mexri to 200 mporei na grafei ws a0roisma duo prwtwn ari0mwn, twn opoiwn to ginomeno den einai asafes.

Epishs to a0roisma S den mporei na einai megalutero tou 54, afou h lush (53, S - 53) den exei asafes ginomeno.

Telos, to a0roisma de mporei na einai ths morfhs p+2 (p prwtos), afou pali h lush (2,p) den exei asafes ginomeno. Oute kai to 51, afou h pi0anh lush (34,17) den exei asafes ginomeno.

Prokuptei, loipon, oti ta mona pi0ana a0roismata einai 11, 17, 23, 27, 29, 35, 37, 41, 47 kai 53. As ta onomasoume 'kala a0roismata'.

Molis o A eipe ston G oti 'To h3era pws den tous 3ereis.', automata o G me ton parapanw sullogismo katalave oti to a0roisma einai kalo. Auto, mazi me to ginomeno, tou epetreye na vrei poioi einai oi ari0moi.

Auto shmainei pws mono mia lush apo autes pou antistoixoun sto ginomeno tou G exei kalo a0roisma. As onomasoume ena ginomeno me auth thn idiothta 'spanio ginomeno', dhl. na exei mono mia lush me kalo a0roisma.

Einai eukolo na diapistw0ei an ena ginomeno einai spanio, an einai sxetika mikro, me analush se prwtous paragontes kai exontas mprosta mas mia lista twn deka kalwn a0roismatwn. P.x. to 28 = 2 x 2 x 7, pi0ana a0roismata 4+7 (= 11, kalo a0roisma) kai 2+14 (= 16, oxi kalo a0roisma). Ara to 28 einai spanio ginomeno.

Molis o G eipe ston A 'Twra tous 3erw !', automata o A katalave pws to ginomeno pou gnwrizei o G einai spanio. Auto to stoixeio, mazi me to a0roisma, tou epetreye na vrei ki autos tous ari0mous. Auto shmainei pws, sto (kalo) a0roisma pou gnwrizei o A, mono mia lush antistoixei se spanio ginomeno.

Edw 0elei aplws ligh upomonh kai upologismo, oxi idiaitera makru, mia kai ta kala a0roismata einai mono deka. Ka0e kalo a0roisma pou vriskoume na exei panw apo mia luseis me spanio ginomeno aporriptetai. Mia kalh proseggish einai na arxisoume apo ta megala kala a0roismata (53, 47,...).

De xreiazetai na e3etasoume OLOUS tous sunduasmous !!! Gia to 53, p.x., prokuptei amesws oti toso to 26x27 oso kai to 25x28 einai spania (afou to megisto ginomeno gia to amesws mikrotero kalo a0roisma 47 einai molis 23x24), opote to 53 aporriptetai.

Gia to 47, omoiws to 23x24 kai to 22x25 einai kai ta duo spania (megalutera tou megistou 20x21 gia to amesws mikrotero kalo a0roisma 41, kai epishs de mporoun na grafoun ws ginomeno orwn me a0roisma 53 - diapistwnetai amesws me analush tous se prwtous paragontes). Paei kai to 47. Kai outw ka0e3hs...

Prokuptei oti to mono kalo a0roisma tou opoiou MONO MIA lush antistoixei se spanio ginomeno einai to 17. Auth h lush einai to 4 + 13, pou antistoixei sto ginomeno 52.

Ara oi ari0moi einai to 4 kai to 13.

Kala na pernate,

Dimitris

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