Solving Congruence Systems: Finding a Number That Satisfies Multiple Remainder Conditions

Math Problem Statement

tìm 1 số, biết: nêu chia 2 thì còn dư 1, chia 3 thì dư 2, chia 4 thì dư 3, chia 5 thì dư 4, chia 6 thì dư 5

Bài toán này có thể được giải bằng cách sử dụng phương pháp đồng dư, cụ thể là hệ đồng dư. Giả sử số cần tìm là $x$ . Ta có hệ phương trình sau:

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Modular Arithmetic
Congruence Systems
Chinese Remainder Theorem

x ≡ 1 (mod 2)
x ≡ 2 (mod 3)
x ≡ 3 (mod 4)
x ≡ 4 (mod 5)
x ≡ 5 (mod 6)

Chinese Remainder Theorem

Grades 10-12

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