A Friendly Introduction to Number Theory
An introductory text designed to entice non-math majors to think mathematically. The reader is gradually led from basic algebra to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing style is informal and includes many numerical examples which are analyzed for patterns and used to make conjectures. The emphasis is on the methods used for proving theorems rather than on specific results.
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What Is Number Theory?
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bad prime Chapter compute congruence x2 conjecture digits Diophantine divides divisible E-primes elliptic curve ep(a equal Euclidean algorithm Euler's Criterion Euler's formula Euler's phi function exactly example Exercise exponent fact Fermat's Last Theorem Fermat's Little Theorem gcd(a gives greatest common divisor infinitely many primes Legendre symbol list of primes look mathematical mathematicians Mersenne primes method Modularity Pattern modulo 13 multiple number of points number theory odd numbers p-defects pairs Pell's equation Pell's equation x2 perfect number perfect square Pigeonhole pigeons points modulo positive integers prime numbers primes congruent primitive Pythagorean triple primitive root modulo product of primes proof prove Quadratic Reciprocity quadratic residue modulo rational coordinates rational numbers relatively prime remainder smallest solution solution to Pell's square modulo square-triangular number successive squaring suppose torsion collection true values verify whole numbers write