From: Θεόδωρος Γαβράς (gavras(@)aias.gr)
Date: Παρ 12 Απρ 2002 - 06:21:00 EEST
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Auti einai i gnomi mou kai zito signomi prokatabolika gia to extra diabasma.
Arxika exo 1 erotisi.:
- Kapia stigmi anafereis oti "Epishs to a0roisma S den mporei na einai megalutero tou 54, afou h lush (53, S - 53) den exei asafes ginomeno."
Pos prokiptei auto? Exeis kanei kapio programma kai san apotelelesma pires auto to dedomeno??
Kai tora i diafonia mas:
Molis diabasa : "A : To h3era pws den tous 3ereis. Oute egw tous 3erw."
kai tin analisi pou ekanes (kai simfono mexri edo) , skeftika orea exo :
x * y = G <=> y = G / x (1)
kai
x + y = A (2)
(Opou A=11, 17, 23, 27, 29,35, 37, 41, 47 kai 53 kai episis
oti isxiei to A den mporei na einai megalutero tou 54)
A = Kalo Athroisma
kai kano ena paradeigma esto oti G = 190.
Kathe fora sximatizetai ena trionimo tis morfis :
a*(x^2) + b*x + c = 0 (3)
H (2) meso tis (1) ginete :
(x^2) - A * x + G = 0 (4)
Apo (3) kai (4) exoume :
a = 1 , b = - A (Kalo Athroisma) kai c = G = 190
Meso tou Excel exo ta akoloutha:
Pithana A a*(x^2) b*x c D Riza 1 Riza 2
11 1 -11 190 -639 - -
17 1 -17 190 -471 - -
23 1 -23 190 -231 - -
27 1 -27 190 -31 - -
29 1 -29 190 81 19 10 (Lisi)
35 1 -35 190 465 28,3 6,7
37 1 -37 190 609 30,8 6,2
41 1 -41 190 921 35,7 5,3
47 1 -47 190 1449 42,5 4,5
53 1 -53 190 2049 49,1 3,9
Etsi loipon i lisi einai to (19,10) me G = 190 kai A = 29
Gia G = 18 ews G = 702 iparxoun 85 ginomena pou exoun ena kai mono kalo athroisma A, simperilamvanomenou tou 52 = 4 * 13.
Ara loipon, otan akoustei "G : Twra tous 3erw !" Ontos tha exei brei tous arithmous.(opou sto sigkekrimeno paradeigma (19,10))
Meta otan akoustei "A : Twra tous 3erw ki egw !" Me tin diki sou lisi tha exei brei tin (4,13)
Ara stis 84/85(ektos tou G=52) periptoseis o G kai A tha exoun brei diaforetikes liseis.
Auto nomizo,ginete dioti:
Otan akougete "A : Twra tous 3erw ki egw !"
Esi ipostirizeis oti :
"Molis o G eipe ston A 'Twra tous 3erw !', automata o A katalave pws to ginomeno pou gnwrizei o G einai spanio. "
Ego nomizo oti kateuthineis tin lisi pros ta ekei, enw den isxiei. Kai auto logo tou oti, an ego eimoun o G tha efarmoza to sistima eksisosewn, opos ekana parapano.
Tora osa gia tin pliri lisi tou grifou den mporesa na katalikso pouthena.
Euxaristo Poli , Gavras Theodor
Parakato akolouthei i lisi apo tin lista.
G : Den 3erw poioi einai oi ari0moi.
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'.
A : To h3era pws den tous 3ereis. Oute egw tous 3erw.
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'.
G : Twra tous 3erw !
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.
A : Twra tous 3erw ki egw !
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.
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