Language: English

Day: 1

r

Pr s tt t st S ts t s r t rt

ts A B S tr s t C S s tt AC = BC s tt S s trr r tr rt ts A B C S tr s t P S s tt PA = PB = PC

tt r trs n > 3 tr sts st sst n ts

tr trs n > 3 r tr sts trr st sst nts

Pr tr trs (a, b, c) st trs s tt t rs

ab c, bc a, ca b

s r 2

r 2 s tr t r 2n r n s t tr

Pr t ABC t tr t AB > AC t ts rr H tsrttr F t t t tt r A t M t t BC t Q t

t s tt HQA = 90 t K t t s tt HKQ = 90 sstt t ts A B C K Q r rt ts rr

Pr tt t rrs trs KQH FKM r tt t tr

s rs ts

r s rt ts

Language: English

Day: 2

tr

Pr r ABC s rr rtr O r t tr Atrsts t st BC t ts D E s tt B D E C r rt

BC ts rr t F G t ts trst s tt A F B C G ts rr t K t s t trst t rr tr BDF t st AB t L t s t trst t rr

tr CGE t st CA

s tt t s FK GL r rt trst t t t X Pr tt X s

t AO

Pr t R t st r rs tr ts f : R R sts tqt

f(x+ f(x+ y)

)+ f(xy) = x+ f(x+ y) + yf(x)

r r rs x y

Pr sq a1, a2, . . . trs stss t ts

1 6 aj 6 2015 r j > 1

k + ak 6= + a r 1 6 k <

Pr tt tr st t st trs b N s tt

n

j=m+1

(aj b)

6 10072

r trs m n sts n > m > N

s rs ts

r s rt ts