ෆර්මාගේ අවසන් ගැටළුව

luxmen

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methana krla thiyenne n=2 thiyena gunayak n>2 ne kiyala pennana ekane.

mulinma n=2 kiyala aragena ai n/2 variable kiyanne??? wichalanaya wenne nene. n=2 . n/2 =1


n=2 wenkota terms 3 kin liyana puluwan. n>2 ehema be . ow eka hari.den aththtama ekada methana ? uththare?
a+b ^n ekak aran ai? me proof eka kiyawddi prashnei mekai kisi galapeemak ne wage denenawa. mage danum mattame awulak wennathi eka :)

Start ekedi n=2 kiyala mama gatthe naha. Sadarana equation ekak gatthe c^n = a^n +b^n meke n nodanna term ekaki. Eka nisa sadarana equation ekaki. n valata sadarana value ekak try kala.
 

luxmen

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Namuth mea proof eke expose nokarapu kotasak mama laga thiyenava. Eya danne , Fermat saha Mama Pamani.
 

luxmen

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maru...
habai aulak thibboth thiyenne methana........

From (1)---- c^n/2<a^n/2+b^n/2
From(2) ----c^n/2<(a+b)^n/2
So-----a^n/2+b^n/2=(a+b)^n/2
(a+b)^n/2 =a^n/2+b^n/2
(a+b)^n=(a^n/2+b^n/2)^2
------Trigonometry mathak kara ganna. a^n/2 and b^n/2 and c n/2 kiyanne right angletriangle ekaka padha. c^n/2 vikarrnaya venava. MEHI THIYENA ASAMANATHA[<] VALIN ADAHAS VENNE NORMAL ASAMANATHAVAYAK [<] NEVE. C ^n/2 < a ^n/2 + b ^n/2 kiyanne VIKARRNAYE [C^n/2] MAXIMUM LIMIT EKA a^n/2 + b^n/2 kiyana ekai. FOR EXAMPLE a <10 saha a MAXIMUM VALUE eka 10 vita, a <10 athara venasak thiyenava.For example a=2 nam a<10---- a < 9 -----a<8------a< 7 -----a <6------a< 5 -----a< 4----a< 3---viya haka. NAMUTH a < 10 kiyanne 10 , a ,vala maximum value eka nam 2< 10 pamanai select kala hakke.
 
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luxmen

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you wrote in your proof

From (1)---- c^n/2<a^n/2+b^n/2 ---(a)
From(2) ----c^n/2<(a+b)^n/2 ---(b)
So----- a^n/2+b^n/2=(a+b)^n/2 ---(c) ???

(a) and (b) are inequalities so how can you say a^n/2+b^n/2=(a+b)^n/2 just because left sides are equal?

It's just like saying
2< 2+4
2< 5+7

so 2+4 = 5+ 7 ????
------Trigonometry mathak kara ganna. a^n/2 and b^n/2 and c n/2 kiyanne right angletriangle ekaka padha. c^n/2 vikarrnaya venava. MEHI THIYENA ASAMANATHA[<] VALIN ADAHAS VENNE NORMAL ASAMANATHAVAYAK [<] NEVE. C ^n/2 < a ^n/2 + b ^n/2 kiyanne VIKARRNAYE [C^n/2] MAXIMUM LIMIT EKA a^n/2 + b^n/2 kiyana ekai. FOR EXAMPLE a <10 saha a MAXIMUM VALUE eka 10 vita, a <10 athara venasak thiyenava.For example a=2 nam a<10---- a < 9 -----a<8------a< 7 -----a <6------a< 5 -----a< 4----a< 3---viya haka. NAMUTH a < 10 kiyanne 10 , a ,vala MAXIMUM VALUE eka nam, 2< 10 pamanai select kala hakke.
 
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luxmen

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Avastha dekedima MAXIMUM values enne. Triangle eka diha baluwama vatahenava. Avastha dekedima MAXIMUM values salaka balenne. C^n/2 MAXIMUM VALUE ekai thiyenne. Dekak thibiya nohaka. So ----a^n/2 +b^n/2 = [a+b]^n/2
 

07sanjeewakaru

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  • Feb 9, 2013
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    ලංකාවෙ අඩා...!
    Avastha dekedima MAXIMUM values enne. Triangle eka diha baluwama vatahenava. Avastha dekedima MAXIMUM values salaka balenne. C^n/2 MAXIMUM VALUE ekai thiyenne. Dekak thibiya nohaka. So ----a^n/2 +b^n/2 = [a+b]^n/2
    kohomada awastha dekenma ekama limit eka denawa kiyanne.....:confused::confused:
    ethana thama wadagathma tharkaya.......oya samanakireema matha thama proof ekama rada pawathinne.........
    mokada asamanatha dekakin samanathawak ganne....
    ethenta hoda pahadili kireemak oona wei.........

    eth meka maru........
    ohoma thaniyama karanan marai......
    oya othana newei inta oone sirawata....:yes::yes::yes::yes::yes::yes::yes::yes:
     

    luxmen

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    kohomada awastha dekenma ekama limit eka denawa kiyanne.....:confused::confused:
    ethana thama wadagathma tharkaya.......oya samanakireema matha thama proof ekama rada pawathinne.........
    mokada asamanatha dekakin samanathawak ganne....
    ethenta hoda pahadili kireemak oona wei.........

    eth meka maru........
    ohoma thaniyama karanan marai......
    oya othana newei inta oone sirawata....:yes::yes::yes::yes::yes::yes::yes::yes:
    Thanks, and Oba educated kenek kiyala penava. MEMA ASAMANATHAVAYAN[INEQUALITIES] DEKAMA RIGHT ANGLE TRIANGLE EKATA CONNECTED. EKA NISA HODIN PARIKKSHA KARA BALANNA. MEMA AVASTHA DEKEDIMA UNIQUE OPPORTUNITY[ONE OPPORTUNITY] THIYENNE. *****NATHNAM RIGHT ANGLE EKA KADENAVA.*****EKA NISAI RIGHT SIDE EKA SAMANA VENNE.
     
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    luxmen

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    ithuru tika Mama expose karanna inne, open Meeting ekakadi. E kivve, for n> 2 , there are no positive integers for a,b,c . MEMA ITHURU EASY PROOF TIKA*****FERMA DANNAVA*****MAMA DANNAVA*****. FERMA TA KARANA GARU KIRIMAK VASAYEN, MAMA ITHIRI TIKA IDIRIPATH KARANNAM, OPEN PUBLIC MEETING EKAKADI.
     

    mag123

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  • Jan 20, 2008
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    Originally Posted by mag123
    you wrote in your proof

    From (1)---- c^n/2<a^n/2+b^n/2 ---(a)
    From(2) ----c^n/2<(a+b)^n/2 ---(b)
    So----- a^n/2+b^n/2=(a+b)^n/2 ---(c) ???

    (a) and (b) are inequalities so how can you say a^n/2+b^n/2=(a+b)^n/2 just because left sides are equal?

    It's just like saying
    2< 2+4
    2< 5+7

    so 2+4 = 5+ 7 ????

    ------Trigonometry mathak kara ganna. a^n/2 and b^n/2 and c n/2 kiyanne right angletriangle ekaka padha. c^n/2 vikarrnaya venava. MEHI THIYENA ASAMANATHA[<] VALIN ADAHAS VENNE NORMAL ASAMANATHAVAYAK [<] NEVE. C ^n/2 < a ^n/2 + b ^n/2 kiyanne VIKARRNAYE [C^n/2] MAXIMUM LIMIT EKA a^n/2 + b^n/2 kiyana ekai. FOR EXAMPLE a <10 saha a MAXIMUM VALUE eka 10 vita, a <10 athara venasak thiyenava.For example a=2 nam a<10---- a < 9 -----a<8------a< 7 -----a <6------a< 5 -----a< 4----a< 3---viya haka. NAMUTH a < 10 kiyanne 10 , a ,vala MAXIMUM VALUE eka nam, 2< 10 pamanai select kala hakke.

    Last edited by luxmen; Today at 03:58 AM.

    =====================================================

    From (1)---- c^n/2<a^n/2+b^n/2 --- (a)
    From(2) ----c^n/2<(a+b)^n/2 --- (b)
    So----- a^n/2+b^n/2=(a+b)^n/2 ---(c) ???

    Still you haven't explain how a^n/2+b^n/2=(a+b)^n/2 from equations (a) & (b) which is based on your further proof.
     
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    luxmen

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    C^n/2 saha C kiyanne rightangle triangles vala Vikarrnayange lengths. a^n/2,b^n/2 and a,b kiyanne ithiri padha deke lengths. inequalities ave meva asuren. Inequalities dekema C^n/2 thiyenava.
     
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    mag123

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  • Jan 20, 2008
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    C^n/2 saha C kiyanne rightangle triangles vala Vikarrnayange lengths. a^n/2,b^n/2 and a,b kiyanne ithiri padha deke lengths. inequalities ave meva asuren. Inequalities dekema C^n/2 thiyenava.

    Let’s say for simplicity D=c^n/2 , A= a^n/2 , B=b^n/2 , T=(a+b)^n/2
    Then
    D < A+B ---(a)
    D < T ---(b)
    Then you say A+B= T from above two??
     

    luxmen

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    Let’s say for simplicity D=c^n/2 , A= a^n/2 , B=b^n/2 , T=(a+b)^n/2
    Then
    D < A+B ---(a)
    D < T ---(b)
    Then you say A+B= T from above two??
    YES BECAUSE WE HAVE COME ACROSS *RIGHT ANGLE TRIANGLE* . DO NOT FORGET RIGHT ANGLE TRIANGLE.INEQUALITIES TAKEN FROM RIGHT ANGLE TRIANGLE.
     

    luxmen

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    WE HAVE COME ACROSS RIGHT ANGLE TRIANGLE. SO C^n/2 < a^n/2+b^n/2 has totally unique values. It is unique[one] . Otherwise right angle breaks.[then it is not a right angle tri angle]
     
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    luxmen

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    Originally Posted by mag123
    you wrote in your proof

    From (1)---- c^n/2<a^n/2+b^n/2 ---(a)
    From(2) ----c^n/2<(a+b)^n/2 ---(b)
    So----- a^n/2+b^n/2=(a+b)^n/2 ---(c) ???

    (a) and (b) are inequalities so how can you say a^n/2+b^n/2=(a+b)^n/2 just because left sides are equal?

    It's just like saying
    2< 2+4
    2< 5+7

    so 2+4 = 5+ 7 ????

    ------Trigonometry mathak kara ganna. a^n/2 and b^n/2 and c n/2 kiyanne right angletriangle ekaka padha. c^n/2 vikarrnaya venava. MEHI THIYENA ASAMANATHA[<] VALIN ADAHAS VENNE NORMAL ASAMANATHAVAYAK [<] NEVE. C ^n/2 < a ^n/2 + b ^n/2 kiyanne VIKARRNAYE [C^n/2] MAXIMUM LIMIT EKA a^n/2 + b^n/2 kiyana ekai. FOR EXAMPLE a <10 saha a MAXIMUM VALUE eka 10 vita, a <10 athara venasak thiyenava.For example a=2 nam a<10---- a < 9 -----a<8------a< 7 -----a <6------a< 5 -----a< 4----a< 3---viya haka. NAMUTH a < 10 kiyanne 10 , a ,vala MAXIMUM VALUE eka nam, 2< 10 pamanai select kala hakke.

    Last edited by luxmen; Today at 03:58 AM.

    =====================================================

    From (1)---- c^n/2<a^n/2+b^n/2 --- (a)
    From(2) ----c^n/2<(a+b)^n/2 --- (b)
    So----- a^n/2+b^n/2=(a+b)^n/2 ---(c) ???

    Still you haven't explain how a^n/2+b^n/2=(a+b)^n/2 from equations (a) & (b) which is based on your further proof.
    --------MATHEMATICALLY EXPLANATION-------[2] COMES FROM [1]. ------ SO comes from [a]. -----now right side should be equal mathematically. Because left side is equal[both inequalities come from one inequality]
     

    luxmen

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    INEQUALITY [2] COMES FROM INEQUALITY [1]. SO IF LEFT SIDE IS EQUAL , THEN RIGHT SIDE SHOULD BE EQUAL .