随信附上我的x光照片以兹证明。
各方授权代表附上签名如下，以兹证明。
IN WITNESS WHEREOF, the duly authorized representatives of the Parties affix their signature below.
兹证明本证明书持有人已获得最高奖在以英语为母语的比赛。
This is to certify that the holder of this certificate has been awarded top prize in the English-speaking contest.
8月22日的国际数学家大会（the InternationalCongressof Mathematicians）上，授予了佩雷尔曼博士最高荣誉——菲尔兹奖（theFieldsmedal），以表彰他对解决庞加莱猜想做出的贡献。 时过三年以后，佩雷尔曼对庞加莱猜想的证明已被证实了正确性。
On August 22nd the International Congress of Mathematicians awarded Dr Perelman its highest honour, the Fields medal, for his solution which, having stood for three years, is now taken as correct.
8月22日的国际数学家大会（the InternationalCongressof Mathematicians）上，授予了佩雷尔曼博士最高荣誉——菲尔兹奖（theFieldsmedal），以表彰他对解决庞加莱猜想做出的贡献。 时过三年以后，佩雷尔曼对庞加莱猜想的证明已被证实了正确性。
On August 22nd the International Congress of Mathematicians awarded Dr Perelman its highest honour, the Fields medal, for his solution which, having stood for three years, is now taken as correct.
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