From: marios-violator (mmarioss(@)x-treme.gr)
Date: Σαβ 27 Μαΐ 2000 - 23:57:03 EEST
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polloi htan autoi pou apanthsan swsta ....
Estw oti arxika eixame a laxana...
Estw b i apostasi meta3u duo laxanwn diadoxikwn...
Afou to sxima einai tetragvno, 8a exoume oti, an sti mia pleura tou
tetragwnou exoume x laxana kai stin alli y, oi apostaseis meta3u tous stin
mia pleura 8a einai sunolika (x-1)*b kai stin alli (y-1)*b...
omws afou einai tetragwno, anagkastika
(x-1)*b=(y-1)*b <=>
x-1=y-1 <=>
x=y
Ara sunolika yparxoun x^2 laxana ston kipo...
Meta 8eloume akoma pros8etontas 311 laxana na einai pali tetragwno...
Omoia opws kai pio panw deixnoume oti arkei x^2+311=z^2, diladi kai o neos
ari8mos laxanwn na einai teleio tetragwno fusikou ari8mou...
Etsi exoume:
z^2-x^2=311 <=>
(z-x)*(z+x)=311
Omws o ari8mos 311 einai prwtos, pou simainei oti sto aristero melos 8a
prepei na exoume anagkastikaQ
z-x=1 kai
z+x=311
(afou z+x>z-x ek twn pragmatwn...)
Ara lunontas to poly aplo systimataki pou proekypse briskoume oti z=156 kai
synepws o zitoumenos x einai 155
Ara arxika ta laxana itan x^2=155^2=24025...
filika,
marios
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