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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 elementary number theory equivalence classes Euler's Theorem eventually periodic Exercise Set exists Fermat's Little Theorem finite given greatest common divisor Hint implies incongruent solutions modulo infinite simple continued least positive Legendre symbol Lemma Let n e linear congruence mathematical induction Mersenne prime modp nonnegative integers notation Note number and let obtain odd prime number ordma Pell Equation perfect numbers perfect square positive divisors positive integer positive solutions prime factorization primitive root modulo proof of Proposition Proposition 1.2 Pythagorean triple quadratic congruence quadratic irrational quadratic irrational number quadratic nonresidue modulo quadratic nonresidues quadratic reciprocity quadratic residue modulo rational number real number relatively prime Section simple continued fraction solvable squares of integers statement is true Student Project variable Wilson's Theorem