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Divisibility and Other Beginnings
The Unique Factorization Theorem
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a₁ abelian addition appears applied arithmetic function assertion assume bound called character coefficients common completely congruence consider constant contains contradiction Corollary counting cyclic defined Definition denote derivation determined distinct primes divides divisible divisor easily element equals equations equivalent established estimate Euler example EXERCISES exists extend fact finite fixed follows formula function Further Gauss given gives hence holds identity implies induction infinitely least Lemma log log log n log x m₁ Mathematical method modulo multiple natural obtain odd prime original polynomial positive integer prime primitive root problem progressions proof Prove provides quadratic rational reduced relatively prime representation require residue classes result satisfies Show side solutions subgroup sufficiently Theorem theory turn values yields Σ Σ