Author Archives: Brent

About Brent

Assistant Professor of Computer Science at Hendrix College. Functional programmer, mathematician, teacher, pianist, follower of Jesus.

A probabilty puzzle

Suppose that we have surveyed a certain population of people, and have determined the following probabilities: The probability that a person likes anchovies is . The probability that a person likes to read books is . The probability that a … Continue reading

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Computing the Euler totient function, part 4: totient of prime powers

I’ve been on a bit of a hiatus as I’ve been travelling with my family for the past month. So here’s a recap. Our story so far Recall that the Euler totient function, , counts how many numbers from to … Continue reading

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Computing the Euler totient function, part 3: proving phi is multiplicative

We are trying to show that the Euler totient function , which counts how many numbers from to share no common factors with , is multiplicative, that is, whenever and share no common factors. In my previous post, we looked … Continue reading

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Computing the Euler totient function, part 2: seeing phi is multiplicative

In my last post, I claimed that whenever and are relatively prime. (Recall that counts how many numbers from to share no factors in common with .) Let’s get some intuition for this by looking at some Chinese remainder theorem … Continue reading

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Computing the Euler totient function, part 1

Recall that Euler’s totient function counts how many of the integers from to are relatively prime to , that is, share no factors in common with . For example, , since only , , , and share no factors with … Continue reading

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Post without words #26

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Chinese Remainder Theorem proof

In my previous post I stated the Chinese Remainder Theorem, which says that if and are relatively prime, then the function is a bijection between the set and the set of pairs (remember that the notation means the set ). … Continue reading

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