## Elementary Number Theory and Its Applications |

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ao;a arithmetic base b expansion bit operations Carmichael number Chinese remainder theorem cipher system ciphertext ciphertext block Computer Projects Write conclude Consequently continued fraction expansion Corollary deciphering diophantine equation divides division algorithm Encipher messages enciphering key Euclidean algorithm Euler pseudoprime Fermat's little theorem following theorem formula function greatest common divisor Hence incongruent solutions infinitely integer relatively prime inverse knapsack problem least positive residue Lemma letters linear congruences mathematical induction modular exponentiation multiplicative nonnegative integer notation number theory numerical equivalents obtain odd prime pairs perfect number perfect square plaintext plaintext block positive divisors positive integers less primality test prime divisor prime factorization prime-power factorization primitive root modulo Projects Write programs Proof prove pseudo-random numbers Pythagorean triple quadratic irrational quadratic residue rational number real number relatively prime residues modulo RSA cipher sequence Show simple continued fraction strong pseudoprime super-increasing transformation