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” x2 + y 2 + 1 = wp

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≡ −y (mod p)

dn>?Bá57>?MÔ1›FH9AEG16Ž414B

0 < x2 + y 2 + 1 ≤ 2 0 < w < p”

365!:;145'FDBG16: _



w

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p−1 2

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+ 1 < p2 ”

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x

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f (x2 − y 2 ) = (x − y) f (x) + f (y)

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149 b 1 

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369;:9;>EGFH9;ŽkE(J?3E




f (−y) = −f (y) ‹I”
_ f (x2 − y 2 ) = (x + y) f (x) − f (y) y

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−y

(x − y) f (x) + f (y)




= (x + y) f (x) − f (y)






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p−1 X 

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1 2 2 2 1 1 1 2

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FHŽš@;BG1…

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1 1 3 3 3 4 6 6 1 2 3 4 4 4 5 6 1 2 2 2 5 5 5 6

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x>y>z>0

a2 x2 b2 y 2 c2 z 2 3 _ + + ≥ (by + cz)(bz + cy) (cz + ax)(cx + az) (ax + by)(ay + bx) 4

µ

µ

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™ >?BG16>4~?1SB

≥ b y

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369;:

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„ J0149

1 (by + cz)(bz + cy)

1 (cz + ax)(cx + az) 1

≥ ≥

Ò

BG>?M

Šx

‹(”

Šä

‹(”

369;: Ý J016LS
(ax + by)(ay + bx)

9;1S“?@;34/DFE< ”

_

> 0

_

Šä ‹

FEádn>A/D/H>6zP5áE(J?34E

S ≥ 13 (a2 x2 + b2 y 2 + c2 z 2 ) ·   1 1 1 _ · + + (by + cz)(bz + cy) (cz + ax)(cx + az) (ax + by)(ay + bx)

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5'FD9;ŽkE(J01 `™ …  ™ 1 3



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z1PŽ41E 1

+



1

+ (cz + ax)(cx + az) (ax + by)(ay + bx) 3 _ (by + cz)(bz + cy) + (cz + ax)(cx + az) + (ax + by)(ay + bx)

(by + cz)(bz + cy)

149 b 1 ”

S ≥

zJ01SBG1 S0

9;16“A@;3S/QFQEx<

1

≥





Šå

3(a2 x2 + b2 y 2 + c2 z 2 ) ” S0

‹

= (by + cz)(bz + cy) + (cz + ax)(cx + az) + (ax + by)(ay + bx) = a2 (xy + xz) + b2 (yz + yx) + c2 (zx + zy) _ + (ab + ac)x2 + (bc + ba)y 2 + (ca + cb)z 2

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S0


≤ a2 x2 + 21 y 2 + 12 z 2 + b2




1 2 x 2

+ y 2 + 21 z 2







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+ 12 a2 + b2 + 21 c2 y 2 + 12 a2 + 12 b2 + c2 z 2 2 2 2 2 2 2 2 2 2 2 2

+ c2

= (a2 + b + c )(x + y + z ) + a x + b y + c z ”

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Ò

Šå

BG>?M

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3S9;:

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n ≥ 3 _ Pn (x) = xn sin α − x sin nα + sin(n − 1)α

3S9;Žš/21

α

FD9

(0, π) ”

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= (sin nα)(x2 − 2x cos α + 1)

_

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dn>?BC>E(J01SBzOFH571 FDB€5(Eƒz189;>EG1E(J?3E a2 > 0 369;:E(J0Ò 1 b >?9;:AFQEGFH>?9 2 d2” 3Sa FQ/H35 _ = a4 = · · · = an = 0 2 2 a + a + · · · + a ≥ 200 3 4 100 z1PJ?3š~?1 ˜4FH9 b 1 dn>?B a2 ≥ a j j = 3 ” 4 ” . . . ” 100 ” 

a2 (a3 + a4 + · · · + a100 ) ≥ a23 + a24 + · · · + a2100 ≥ 200 ”

_ 5(FH9;ŽE(JAFH5†FD9;16“A@;3S/QFQEx< E(J01 zJAF b JPFDMNK?/DFH1S5’E(J?3E ≥ 200/a2 ” `™ · · ·+™ a100  9;16“A@;3S/QFQEx< d23 b E†E(J?3E 36a9;3… : +E(J0a1 4 + z1P>0LAE€3SFD9 a1 ≥ a 2 ” ” a1 + a2 + · · · + a100

200

200

≥ a1 + a2 + ≥ 2a2 + a2 a2 r _ 200 ≥ 2 (2a2 ) = 40 a2

9 57K;1 b EGFD9;Ž›E(J01OFH9;1S“?@;34/DFEGF2145!3L0>S~?1 z1P‡;9;:E(J?3E 0 3E€EG34FH905 a1 + a2 + · · · + a100 FQE€58M8FD9?FHM@;M ~A34/D@Z1R>Ad FDd369;: ” >?9?/<|FQd 3S9;: 40 _ a1 = a2 = a3 = a4 = 10 a5 = a6 = · · · = a100 = 0 )N L#HL#HONSY'E'[        0\     MVOCMG MH9V/NZH'L  E#J[E#L        V'C [    &   B   J0L/P/N F CME#C   CVOLIFQP   CC9L JP9G P'L#K J@F V\  E#JE TWVOL H'CMEF CMG0H  NZE'KZE L#HONZP9K FZH'C\  E#LLWL/P RE#L#KQE'[-K ME QHON NZHRTXF C  9E#C E#J@VON F IVRK FSH'CH )K ME JH 'NSE
!    V'JE JE#V/N aCM2['FS.K FS.H'.CL an 1 G0H' CP E#J@L  CM[ K ME =F C9F P  Y#V/NQPREH

L/P IE'GIKDKZH=K  aE 







a1 + a2 + · · · + a n

a1 ≥ a2 ≥ · · · ≥ a n

2 2 a2 1 + a2 + · · · + a m

 EK ME#C


2 2 a2 m+1 + am+2 + · · · + an

JH9GIE'E'[E'[=KZH=['F L#GP'LLXL#H  E




VOJ:K FSG:P/N VOJWGQVOL#E#L H
K  E

≥

0



  RE#CME#J@V/N+ P9E#L#K FZH'C\ ≥

≥

A B

   

    ! V"$%"&D') *, %"&{&  #'>&{&{2=947 s) „?: A „H) 96† „<'( Š4„ '( &? V„w;x,7) 91;H'D :H"1"7 I C . KDT n ∈  J
W TVL n > 1 IM G ` _ (K T ( )  n P G n T = x = (x , . . . , x ) ∈ x =1 x > 0 gASd j = 1 I . . . I n I1M `

n

1

n

j

j

KDT p I q I r ∈ Tn X#[!Z#L TVLMT P √qj rj < P √pj rj j=1  j=1  d]SNK Sdq`WEX#p6d]SNK O MDP Pn pq (r + p ) < Pn pp (r + p ) I j j j j j j j=1 j=1 OAa PfgASdvM _k_ λ ∈ [0, 1] I n

n q X

j=1

n

qj (λrj + (1 − λ)pj ) <



j=1

n q X pj (λrj + (1 − λ)pj )

j=1



 ä ‘ '.;BG>?K;>?5*14B  5PBG14MN3SB(‰654؛ŠH3 FD5CE(J01N57K;1 b FD3S/ b 36571N>AdrŠnL zOFQE(J 1 _N„ JAFH5P“?@Z145*} b >?9 2 EGF2>?9FH5 b >?909;1 b EG16:…zOFQE(JK;BG‹ >?K;1SBÓEGF2145k>AdZE(J01˜6J?3J?57J?3J?‹ 3S9?FqMÔ1šλ EIBGF = 3MÔ1šEIBGF b Tn ” FHM8KZ>?BÓEG3S9AErdn>?BáK;>?K0@0/D34EGFH>?9NŽ41S9;1šEGF b 5 _  & "? ;% 7

),

!$



D;*U1

!+-




:. &X&.2('1.


.2

:(

0*-1

/ &'1.23 "

3;*=<-> A

 " '4.2

ˆ 1k5*J0>6zgE(J?34E’ŠnL FH5 EIBG@Z1ƒzJ01S9 zJAF b JPFDMNK?/DFH1S5 E(J?34E†ŠH3 FH5†3S/D5*>›EIB€@Z1 _ ˆ 1kE(J01S9‹ 57J0>6z J0>6zaEI> n b >?= zJ01S9 905IEI2BG”@ b Er1 S36M8K0/H1S5áEI>…K;BG>4~?1C‹ E(J?3ErŠ23 3S9;: nd234=/H571k 2 zJ01S9 ‹ _ ŠnL 3SBG1O ‹ n≥3 >?B /21šE :01S9;>EG1›E(J01O5(E€369;:?36BG:FH909;14BrK0BG>0:?@ b EáFH9 n _  1šE Ò p” q ∈  n ” p·q  Sn =

5

.A36BÓEŠnL

(

‹

x = (x1 , . . . , xn ) ∈

/



n

369;: dn>?B j = 1” . . . ” n” xj > 0

n P

x2j j=1

FH5!1S“?@0F ~A3S/H1S9AE†EI>…E(J01OK;BG>?K;>?5'FEGF2>?98L;1/2>6z8Ø

=1

)

_

_ d 1šE zOFE(J 5(@ b J8E(J?3E n∈ n>1 p” q ” r ∈ q · r < p · r” qSn zOFQE(J b >?8 M KZ>?9;149AEG5›ŽšF~?149‚LS< dn>?B!5*>?MN1 s ∈ Sn sj = λrj2 + (1 − λ)p2j _ E(J0149 λ ∈ [0, 1] ” q·s6zE(J?3EáE(J01K0BG>?KZ>?5(FQEGFH>?98FD5EIBG@Z1Odn>?B _ >?B b >?9~?1S9?FH1S9 b 1 n=2 Ò z1›BG16Ž3SBG:81S3 b J z1›57161 ” n L;>E(J…3653k~?1 b EI>?B†369;:3653OK;>AFH9AE _-ˆ J01S9 p ∈  n = 2 ” E(J?34E 36BG1ƒ3S/Q/>?9CE(J01ƒ@;9?FQE b FDB b /21ƒ369;:›FD9CE(J01ƒFD9AEI14BGFH>?B->Ad6E(J01‡ZB€5IE-“?@;36:0B€3S9AE _ p ” q:;” 14r9;”>sEI1PE(J013 b @?EG1369;Žš/H1L01EÓz1S1S98~?1 b EG>?B€5  1E 3S9;: _C„ J01S9 q >?9?/ <8FDd q <EIB€p@Z1 · rFQd

>?Bƒ16“A@0F~A34/2149AEG/p< FDd-3S9;pc := zJAqF b ·J8rFH5ƒ c c c c ” ” ” p r < q r cos p r > cos q r 369;:>?9?/ <FDd FH5 b /2>?571SB-EG> E(J?3S9EI> _ ˜4FD9 b 1 r p dn>?Bƒ34/D/ z15*1S1PE(J?3E FD5k>?98E(J01…36qB b L01EÓz1Smin{p 1S9 369;j :” rj }_!„ ≤JA@;s5 j ≤ FDmax{p 5 b /2>?571SjBᔠEGr> j } j ” s p r ” s p _ E(J?369EI> J01S9 b 1 ” q q·s6zz1 b >?905(EIB€@ b EO369U1 S3SMNK?/218EI>{5*J0>6zE(J?34ECE(J01=K0BG>?KZ>?5(FQEGFH>?9µ36L;>4~?1ÔFD5 ?Ú'u 0uAÛ

u6ã 369;:ÔFDd





d23S/D5*1!dn>?B

n=3

_-„ 3‰61

p=  „ J0149 369;: 1 p” r ” s = ,









_ 3S9;: 1 1 1 1 1 1 ” r= √ ,√ ,√ ” λ = 21 √ ,√ ,√ 2 3 3 3 3 √ 6 36BG13S/Q/ƒ>?9µE(J01@;9?FE57K;J01SBG1‚3S9;:UFH9µE(J01 5 1 √ ,√ 2E(J?334EƒFH5 3 E(J01*<3SBG13S/Q/±FH9 _ >EI1E(J?3E FH5C9;>E>?9

HF 9AEG1SB€F2>?B>Ad±E(J01‡;B€5(E> b EG3S29AE s 36BG1›3S/Q/Z>?9 E(J01PŽBG1434E b FHB b /H1kE(J?34ErŽ4>0145áE(J?BG>A@ZŽ4J ” 3S9;: 5'FD9 b 1kE(J0S 1S5731kE(J?BG161OK;>AFH9AE€5 p r ” _ E(J01P573SMÔ1›/D34EGFEG@Z:;1kzOFQE(J x3 = √13 Ý >?905(F2:01SB-E(J01 b FHB b /H1 >?9 zOFE(J b 1S9AEIBG1 K;3S575(FH9;ŽƒE(J?BG>A@ZŽ4JE(J01CK;>AFH9AE _ C1S19AEGFDBG14S/ <› 3 >?9 Š  >EI1áE(J?3E 9;1S16:C9;>EZ/QF21 5(FH9 b 1 r FH5->?9?/< 1 >Ad4E(J01r@;9?FQE57K;J01SBG1 p_ C S 1 3 „ JAFD5 b FDB b /21ƒ:?F ~?FH:;145 FH9AEG>EÓz>CBG1SŽšF2>?905 >?9;1 #7FH905(SF23:01 % E(J01 b 8FHB b /H1!ŠQE(JAFH9;‰k>Ad3ƒKZ>A/D36B‹ S 3 b 3SK 369;:Ô>?9;1 #Ü>A@?EG5(F2:01 % _ ˜4FDM8FQ/H3SBG/ < E(J0” 1 b FDB b /21 >?9 zOFE(J b 149AEIBG1 K0365'5'FD9;Ž E(J?BG>A‹ @ZŽ4JNE(J01…KZ>AFD9AE :?F ~?FH:;145 FH9AEG” >8EÓz>NBG1SŽšF2>?C9025 _ ˜4FDS 9 3b 1 :0>Ô9;s>E/DFH1>?9 3ŽBG1S3E b FDB b /21 3Sp9;: 3SBG1S9;3>EáEG3S9;Ž41S9AEƒ3E _r„ JA@;5 E(J01SpBG” 1r3S” BGs1KZ>AFD9AEG5k>?9 ” C C S3 1 2 36BIL?FEIB€36B€FD/ < b /H>?5*1kEG> E(J?3Eá36BG1O>A@?EG5(F2:01 3S9;:pFH905(F2:01 ” _†Ý /21436B€/< ” p C C q · r < p 1 2 3S9;: FDd 369;:>?9?/ <ÔFDd FH5C>A@?EG5(F2:01 FDd 369;:>?9?/ <ÔFQd FH5FH905(F2:01 · r_ q C ” q · s > p · s q C2 1  149 b 1 FEr5( @  b 1S5rEI>…E€3‰61 EI>8L01P3S9<85(@ b JKZ>AFD9AE _ ” 9 b /H>?5'FD9;Ž z1…BG1SM836qBI‰E(J?3EE(JAFH5kMN1E(J0>0:z>?B(‰65dn>?Bƒ369369< ” n>3 

 ä 

³

Lµ

¸ O¸¹ _  ä ‘‘ÞÌرS‘  $&? 66‘ . M>31';. %
4&  '+,/'+*-1' 3,":?)* ” > '  /'1!>. _ 1E 

a” b”

369;:

c

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>. W ?  .'?  ";*=<-> A


' 




≥ 3 a3 b + b 3 c + c 3 a

3 &



&+

4
 . ":? '*   34& (',!

Nµ

  "? 3 %
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?

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 ('

(a2 + b2 + c2 )2 − 3(a3 b + b3 c + c3 a) ≥ 0

1E

_

E = (a2 + b2 + c2 )2 − 3(a3 b + b3 c + c3 a) a = x”

„ J0149



(


_

I  5 3!"("/ " '+*

 &'4. 3 (" " '




>EG1›E(J?3E†E(J01ŽšF ~?1S9FH9;1S“?@;34/DFE<FH5!1S“?@0F ~A3S/H1S9AE†EG> 



/D.-'4 0" * <3 

L;1OKZ>?5(FQEGF ~?1OBG1S34/Z9?@;MÔL01SB€5 _ .;BG>S~?1CE(J?34E

a4 + b 4 + c 4 + 2 a2 b 2 + b 2 c 2 + c 2 a2

³

@*

>. 3 + ! 3!"

369;:

b = x+p”



_

1E

c = x+q

_

34dDEI14Br5*>?MN1O5'FDMNK?/DFQ‡ b 34EGFH>?905  z 1›‡;9;:E(J?34E ” ”

E = E(x) 

16Ž3SBG:?FD9;Ž

= (p2 − pq + q 2 )x2 − (p3 − 5p2 q + 4pq 2 + q 3 )x E(x)

3S5!3“A@;3:?B€34EGF b FD9

_

+ (p4 − 3p3 q + 2p2 q 2 + q 4 )

x”

FEG5!:?FD5 b B€FHMFH903S9AEáFD5

∆ = (p3 − 5p2 q + 4pq 2 + q 3 )2

− 4(p2 − pq + q 2 )(p4 − 3p3 q + 2p2 q 2 + q 4 )

= −3(p6 − 2p5 q − 3p4 q 2 + 6p3 q 3 + 2p2 q 4 − 4pq 5 + q 6 ) = −3(p3 − p2 q − 2pq 2 + q 3 )2

_

3S9;: 2 dn>?B3S/Q/ ˜4FH9 b 1 FQE!dn>A/D/H>6zP5kE(J?3E ∆ ≤ 0 p − pq + q 2 ≥ 0 ” E(x) ≥ 0 _ x )N L#HUL#HONSY'E'[        B    J0L/P/N F CME#C   CVOLIFQP  SC9CL JPRG P'L#K J@F V WVOCM[K  E JH H'L#E#J#\ ME#JET E#JE3LIF F CMG0H'J0JE'GKL#HONQPRK FSH'CLDV'C [ H'C E3F C GIH  NSE'KQEXL#HONZP9K FZH'C\ HPOJ3H MK ME3F CMG0H'J0JE'GK  T RFZG  F L-KZE'G9C9FSGQV/N N UF C GIH'J0JE'GIK  L#HONQPRK FSH'CL VR[EK ME GIH'C Y'E#CRFZE#C KWV'LL/P K FSH'C K VRK b G≤ LIF C GIE K MEXJ@F MK+LIFS[E H K ME!OFSY'E#CF C E +P'V/N FSK H'LL#E#LL#aE#LX≤ H'CRN 

GQN FZcGL   E'K J J@VRK  E#J3K 9V'C GIH  NSE'KQE L   E'K J +\ JE'E3L#HONZP9K FZH'C9L
'VRY'E TXFSK  HP9K JH9H K MEWTWJH'C L#K VRKQE E#C KMK VRKME +P'V/N FSK MHONS[ L;F 9VOCM[ EOYOE#C K MHP   ( K MEOFSY'E#C JH ) 'NZE ['FS[UC H9K3VO L QH'J K  E-[E'KZE#J =F C9V9K FZH'C H XK  E H'C9N F

E +P'V/N FSK a GQVO=L#E#bLO\ = c @K F LGQNSE#V'J JH  K M E QE#VRK0POJE'[L#HONZP9K FZH'CUK VRK
K  EVOLL/P  K FZH'CUK VRK   VOCM[ VOJE H'LIFZK FZYOEWF L c L/P E#J P9HPOLO \
P9K ML#K J@V'C 9EN =E#C HP MC H H'C E HOF C KQE'[=K RF L HPRKDE N FZGZFZK N a\ b  E JH H'L#E#J!OV9YOEV H'JE G0H  N FSGQVRKQE'[=VOCM[=L#H 9F L#K FSGQVRKQE'[ JH9H 3P'LIF C -G0H  NZE =CMP  E#J@L V'C [ J@F =FSK FSY'E JH9H9K L H XPOC9FSK \ LIF C  K RF LV JH'VRG  E TWV'L V 'NZE KZHU[E'KZE#J =F C E K VRK3K  E E +P'V/N FSK

MHONS[ L F DV'C [H'CRN =F XEFSK  E#J H'J QH'JL#H  E GIH'C9L#K VOCMK XT E VRY'E  + z)  MVOCMa[ = b = c 2 F C VOC& Gk GQN FZG3H'J[E#J aT M=E#Jk(1 E + z 2πi/3 2 b = k(1 + wz + w z) c = k(1 + w z + wz) ( √ ;V'C [ \ ) DT E=K V 9wE = e VOCM[ 1 1 z = √1 cos θ θ = −3 Arg(2 + 6w) = − 3 Arg(−1 + 3 3i) k = 1 P'L#E K ME 7V JH 'F  VRKQE YVONZP9E ◦ DT E L#E'E K 9V9K (a, b, c) ≈ (1.629, 1.048, 0.323) H'JXV'C

θ ≈ 33.63 G GQN FZG E#J PRK VRK FSH'CUK  E#JE'H 0\ BG1S34/















































































 ä6ä F  VO N ;E#CMG E

J@VOL#HRY 
H  'V CRF V DL#E#C K;F CUV-G0H   E#CMK;F CM['FSGQVRK F C  K VRK;F CH'C E=H )K ME
 F LL/PRE#L=H 3 B GKZH9H'C VRK  E V9K FZGZVON VO V 0F CME  E JHRYOE'[ K ME QHON NSHRTXF C   H'JE 9E#C E#J@VON
F CME +POVON FZK


QH'J    V'C [  
K ME#C 




xk > 0

k = 1 2 ... n α

T ME#JE

n X

α β>0

x4 k +β

k=1

n X

k=1

2 x2 k xk+1 ≥ (α + β)

n X

k=1

x3 k xk+1



\  EG:POJ0JE#CMK JH 'NSEF L K ME L E'GZF V/NGQVOL#E T ME#C  MVOCM[ \   J:KZH'V I EWVOCM[ OV CMH9K ME#J
L#HONZYOE#J
JE VOJ E'[ K VRK;K ME!OFSY'E#CF C E +P'V/nN FSK =

QHO3N NZHRαTW= L J1H  K  EXβFS[=E#CM2K FZK

xk+1 = x1







4(a2 + b2 + c2 − ab − bc − ca) (a + b + c)2 − 3(a3 b + b3 c + c3 a) =

(A − 5B + 4C)2 + 3(A − B − 2C + 2D)2



T M E#JE   ;VOCM[ \ 3 3 3 2 2 2 2 2 2 RNZE#VOJ@N A XYO= E#J@F a /F C + UK b9F L+FZ[cE#C K FSB K =  a9V'bC [ +F L bV c QH'+J =cFZ[ aV 'C NZE K =VOL Mab \  +E=bc E'['FZKZH'+J ca K0POJ0CME'[ KZH D  = 3abc  QH'J MEN VOCM[ QHPOCM[-K MEFZ[E#C K FSK KQH EGIH'J0JE'GIKI\ C QH'J:K0POCVRKQEN 
K  E L#HONSY'E#J@L ['FZ[ CMH9KDE N V/F C MHRT K ME

V'J0J@FSY'E'[V9KDK 9F LXV V 0F C  FZ[E#C K FSK \   J:KZH'V IE  E#CMK FZH'C E'[ K 9V9KK  E /FZYOE#C F CME +POVON FZK 9V'L)V E#VOJE'[ E QH'JEWVOL JH 'NSE

  H'C VR E  H

MV E'K V VRKQE VRK FSGQ
V 
  F C 
H  V'CRF VOC +F C K  E QHON NZHRTXF C  E +P/FZYVONSE#CMK QH'J 


( ) ( )   V'C [ VOJE JE#V/N+CP E#J@L 
K ME#C














a b







c

a2 (a − b)(a − 2b) + b2 (b − c)(b − 2c) + c2 (c − a)(c − 2a) ≥ 0

 HRT EOYOE#J  E L#K VRKQE'[=K 9V9KMVL#HONZP9K FZH'CUTWVOLXCMH9K P 'N F L  E'[ K ME#JER\







 g  ] D    D !V"$%"&D') *, B9\\, u. "41&("417 Š4„ '( &V„w;x,‚" C ' B>†41&;q„<…]57c#')6I 'D „H…{;<"47 C  94B) /.  @6 „?& „?&‹@B'D]7 Š4„ '( &V„w;x,=" %'(€D„x4197  '>€„E4697Š0(v o y X(IBJ
WkTVL  „E4ƒ)6'(#'‹:?:E9 M G ` TVL1K  '( 4 9 ‹;u&\$ƒ@ƒ'(#' MDTsLM G `ƒI S G K 1 L  K ‹ X = K 1 ` M Z\M _ G `6S^ MZ]T][6M _ X{p6_ L1Kd WxZ]M _ Z\^ S G XVT\d [!G Z]T]WxS G X(IDG [6XVW G6^ M G X#p!L1Kd]WEZ\M _ d][ _ _ Kd!T]Ss`1d M(J TVL1K Z\Se  p KDT]K d]KMDT Z\WEd]Z K
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WkTVL+Z\K G _ T\d]K A M G `+_ d M`G Wk[6X BC O G ≤ π2 IX{M y IS G M [ G W TuX{p6L1K^ d]K>_ P W NK MXVWEe+p K
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xr−3 + y r−3 − xr − y r = 2S + T + xr−3 (1 − x)2 + y r−3 (1 − y 2 )2 ≥ 0 ”

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