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IMO2016香港试题英文版


Language: English Day: 1

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?t???? A ??? C ? P???t D ?s ???s?? s??? t??t DA = DC ??? AC ?s t?? ??s??t?r ?? ∠DAB ? P???t E ?s ???s?? s??? t??t EA = ED ??? AD ?s t?? ??s??t?r ?? ∠EAC ? ▲?t M ?? t?? ???????t ?? CF ? ▲?t X ?? t?? ????t s??? t??t AM XE ?s ? ??r???????r?? ????r? AM EX ??? AE M X ?? Pr??? t??t ????s BD? F X ? ??? M E ?r? ?????rr??t? ???? ??? ??s?t??? ??t???rs n ??r ????? ???? ???? ?? ?? n × n t???? ??? ?? ????? ??t? ??? ?? t?? ??tt?rs ■? ▼ ??? ? ?? s??? ? ??② t??t?
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?? t?? ??tr??s ?r? ■? ??? t??r? ?r? ▼ ??? ??? t??r? ?r? ??

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▲?t P = A1 A2 . . . Ak ?? ? ?????① ???②??? ?? t?? ?????? ??? ??rt???s A1 ? A2 ? ? ? ? ? Ak ???? ??t??r?? ???r????t?s ??? ??? ?? ? ??r???? ▲?t S ?? t?? ?r?? ?? P ? ?? ??? ??s?t??? ??t???r n ?s ????? s??? t??t t?? sq??r?s ?? t?? s??? ????t?s ?? P ?r? ??t???rs ????s???? ?② n? Pr??? t??t 2S ?s ?? ??t???r ????s???? ?② n?

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Language: English Day: 2

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? s?t ?? ??s?t??? ??t???rs ?s ?????? ?r??r??t ?? ?t ???t???s ?t ???st t?? ??????ts ??? ???? ?? ?ts ??????ts ??s ? ?r??? ???t?r ?? ?????? ??t? ?t ???st ??? ?? t?? ?t??r ??????ts? ▲?t P (n) = n2 + n + 1? ???t ?s t?? ???st ??ss???? ????? ?? t?? ??s?t??? ??t???r b s??? t??t t??r? ?①?sts ? ????????t??? ??t???r a ??r ????? t?? s?t
{P (a + 1), P (a + 2), . . . , P (a + b)}

?s ?r??r??t?
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??? ?q??t???
(x ? 1)(x ? 2) · · · (x ? 2016) = (x ? 1)(x ? 2) · · · (x ? 2016)

?s ?r?tt?? ?? t?? ???r?? ??t? ???? ?????r ???t?rs ?? ???? s???? ???t ?s t?? ???st ??ss???? ????? ?? k ??r ????? ?t ?s ??ss???? t? ?r?s? ?①??t?② k ?? t??s? ???? ?????r ???t?rs s? t??t ?t ???st ??? ???t?r r?????s ?? ???? s??? ??? t?? r?s??t??? ?q??t??? ??s ?? r??? s???t???s? ???r? ?r? n 2 ???? s?????ts ?? t?? ????? s??? t??t ???r② t?? s?????ts ?r?ss? ??? ?? t?r?? s?????ts ???t ?t ? ????t? ●??? ??s t? ????s? ?? ???????t ?? ???? s?????t ??? ????? ? ?r?? ?? ?t? ?????? t?? ?t??r ???????t? ???? ?? ???? ???? ??s ????s n ? 1 t???s? ???r② t??? ?? ????s? ???? ?r?? ???? ???????t??② ???? ??r??r? t? t?? ??①t ??t?rs??t??? ????t ?? ?ts s?????t? ?r??s ????r ?????? t?? ??r??t??? ?? t???r ????s? ●??? ??s??s t? ????? t?? ?r??s ?? s??? ? ??② t??t ?? t?? ?? t??? ???? ???r ?????② t?? s??? ??t?rs??t??? ????t ?t t?? s??? t????
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