As Jack listened intently, Nancy's exposition on the Chinese Remainder Theorem carried him into the realm of intricate number symphonies and harmonic congruences.
"Consider the enchanting elegance of the Chinese Remainder Theorem," Nancy began, "where the dance of numbers unveils its magical symphony—a melody that resonates when two relatively prime integers, m and n, converge in the realm of congruences."
"In its wondrous splendor," she continued, "the theorem unfolds a harmonious narrative—a testament that the system of congruences, such as x ≡ a (mod m) and x ≡ b (mod n), always orchestrates a symphony of solutions, weaving integers x into a melodious alignment."
"Moreover," she elucidated, "these solutions find their unique expression—a captivating cadence of the form x ≡ c (mod mn), where harmony flourishes in the convergence of m and n."
"As we traverse through exercises that beckon the mind," Nancy elaborated, "we encounter numerical puzzles seeking the exquisite harmony within the realm of congruences."
"the search for x, resonating within the congruences x ≡ 3 (mod 4) and x ≡ 5 (mod 9), reveals a melodious harmony amid these rhythmic constraints."
Venturing further, beckons us with equations expressing a rhythmic dance, coaxing x through the cadences of x − 3 ≡ 4 (mod 2) and 4x + 2 ≡ 0 (mod 5)."
And in the enchanting quest for the smallest positive value leads us on a mystical journey where n, guided by the constraints of congruence—n ≡ 4 (mod 5), n ≡ 3 (mod 6), and n ≡ 2 (mod 7)—seeks its serene alignment."
"In this intricate dance," she concluded, "the exercises serve as melodic keys, unraveling the harmonic mysteries, and guiding us through the majestic world of modular arithmetic."
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然後按「加至主畫面」