Calculations with congruences,Bézout's Lemma et al.
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Mathematics, the study of patterns, unveils the universe's hidden order, from prime numbers to fractals. It's a logical framework for reasoning and modeling reality, exemplified by prime factorization's role in cryptography and infinity's profound implications. Beyond theory, mathematics drives innovation through algorithms, powering technology from online searches to complex optimizations. Probability and statistics provide tools to navigate uncertainty. The beauty of mathematics, seen in fractals and elegant proofs, reflects human ingenuity. Exploring mathematical concepts is a journey into reason, revealing the interconnectedness that shapes our world.