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1) Show that ∀a, b, c ∈ ℤ, a|b ∨ a|c =⇒ a|bc. 2) Consider the...

1) Show that ∀a, b, c ∈ ℤ, a|b ∨ a|c =⇒ a|bc.

2) Consider the integers 3213 and 1386.

a) Show the steps of the Euclidean Algorithm for 3213 and 1386.

b) Show the steps of the Exended Euclidean Algorithm for 3213 and 1386.

3) Notice that as we compute the solution to a set of congruences with Chinese Remainder Theorem, our moduli increase in size at each step. This means that each computation will require numbers of greater size. Can you reorganize the solution process to reduce the size of numbers needed at each step?

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