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Mathematics — 2025, Undergraduate
This study assessed algebraic structure methods for solving congruence problems. Linear and quadratic congruences were solved using modular arithmetic techniques, and solutions were verified and compared across methods. The findings revealed that structured methods, including the Chinese remainder approach, produced correct and efficient solutions, with systematic handling of non-unique cases. The study observed that understanding modular structures reduced computation time. It recommends emphasising structural approaches in teaching number-theoretic problem solving.
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