Practice Exam 2

Problem (1) Using Mathematical Induction prove,

Problem (2) Using Mathematical Induction prove, is divisible by

Problem (3) Show the product of two integers of the form is of the form

Problem (4) Show that the product of three consecutive integers is divisible by 6.

Problem (5) Show that any prime of the form is also of the form

Problem (6) Show that there are infinitely many primes.

Problem (7) Show that divides for any integer and any positive integer

Problem (8) Show that

Problem (9) Apply the Euclidean Algorithm to find

Problem (10) Apply the Euclidean Algorithm to find

Problem (11) Find the unique factorization of

Problem (12) Find the unique factorization of

Problem (15) Show that is divisible by 48 for all positive integers

Problem (16) Apply the Euclidean Algorithm to solve Then find all solutions.

Problem (17) Show that if and are mutually prime integers, then

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