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How can I prove that I won the prize without a certificate of mathematical modeling competition?
You can apply to the original organizer for a replacement or issue a certificate.

The certificate of mathematical modeling is an award-winning certificate issued by the national mathematical modeling competition for college students. The National Mathematical Modeling Competition for College Students was founded in 1992 and held every year. It has become the largest basic subject competition in domestic universities and the largest mathematical modeling competition in the world. In 20 18, 1449 colleges/campuses and 42 128 teams (38,573 undergraduate teams and 3,555 junior college teams) from 34 provinces/cities/regions (including Hongkong, Macau and Taiwan Province) and the United States and Singapore signed up for the competition.