Elementary Number TheoryThis is a straightforward, up-to-date number theory text with a slight emphasis on applications (as noted by inclusion of a final chapter eight on same). All definitions, theorems, and proofs are accompanied by examples so as to be as detailed as possible. Class testing has been conducted to solicit student and professor feedback. |
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a₁ Algebra arithmetic functions Assume Chapter compute congruence x2 congruent modulo conjecture continued fraction expansion contradiction convergents Corollary Definition denoted desired statement Diophantine equation distinct prime numbers dy² elementary number theory equivalence classes Euler's Theorem eventually periodic Example Exercise Set exists Fermat's Little Theorem Find finite given greatest common divisor Hint implies incongruent solutions modulo infinite simple continued inverse least positive Legendre symbol Lemma linear congruence mathematical induction Mersenne prime nonnegative integers notation Note number and let obtain odd prime number ordma Pell Equation perfect numbers perfect square positive divisors positive integer prime factorization primitive root modulo proof of Proposition Pythagorean triple quadratic congruence quadratic irrational quadratic irrational number quadratic nonresidue modulo quadratic nonresidues quadratic reciprocity quadratic residue modulo r₁ rational number real number relatively prime Section simple continued fraction solvable squares of integers Student Project Wilson's Theorem x₁