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Learning Goal: I’m working on a discrete math question and need an explanation and answer to help me learn.

Problem 9.43
We define the sequence of numbers
an = {1, for n ≤ 3
an−1 + an−2 + an−3 + an−4, for n > 3
Use strong induction to prove that rem(an, 3) = 1 for all integers n ≥ 0.

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Problem 9.84 Modified
The RSA algorithm shows how to generate keys, distribute the keys, encrypt information using
the keys, and decrypt information using the keys. When analyzing an algorithm involved in the
communication of sensitive information, it is helpful to investigate security weaknesses. For
example, it would be trivial to decrypt information encrypted using RSA if the factorization into
two primes of n in the public key was known. Use the quadratic formula to show that if you know
n, φ (n), and that n was the product of two primes, then you could easily factor n.

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