Insights into Mathematics | Tips and tricks for computing cyclotomic polynumbers | Famous Math Problems 20d | N J Wildberger @njwildberger | Uploaded 4 years ago | Updated 2 hours ago
We give some of the main tools for explicitly computing cyclotomic polynumbers, having pointed out some of the logical difficulties both with their definition and more importantly their irreducibility in the previous lecture. To illustrate some of the ideas, we tackle the challenge of getting at Phi_1001.

An important ingredient is the Euler totient function which counts the number of natural numbers less than or equal to a natural number n which are relatively prime to it. In general, the prime power decomposition of n has a lot to do with the calculation of Phi_n.

Video Contents:
00:00 Key fact about cyclotomic polynumbers
02:34 More facts ( empirically at least)
06:00 Examples of cyclotomic factorizations
13:07 Challenge: find Phi_1001
19:12 Explicit value for Phi_91 and Phi_143

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