mini challenge: find the smallest cosine of an integer

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mini challenge: find the smallest cosine of an integer

10-21-2021, 01:09 PM

Post: #8

Albert Chan Offline

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RE: mini challenge: find the smallest cosine of an integer

(10-21-2021 12:01 PM)Albert Chan Wrote: With convergents fully reduced, even numerator guaranteed odd denominator.

2 neighboring convergents, p1/q1, p2/q2, we have

p1*q2 - p2*q1 = ± 1 // or, gap = |p1/q1 - p2/q2| = 1/|q1*q2|

If g = gcd(p1,q1) ≠ 1, RHS must be multiples of g, contradict above identity.
Thus, convergents always fully reduced.

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Messages In This Thread

mini challenge: find the smallest cosine of an integer - EdS2 - 10-19-2021, 10:23 AM

RE: mini challenge: find the smallest cosine of an integer - Albert Chan - 10-19-2021, 11:33 AM

RE: mini challenge: find the smallest cosine of an integer - PeterP - 10-19-2021, 11:58 AM

RE: mini challenge: find the smallest cosine of an integer - Albert Chan - 10-19-2021, 01:30 PM

RE: mini challenge: find the smallest cosine of an integer - Albert Chan - 10-19-2021, 02:44 PM

RE: mini challenge: find the smallest cosine of an integer - EdS2 - 10-21-2021, 09:44 AM

RE: mini challenge: find the smallest cosine of an integer - Albert Chan - 10-21-2021, 12:01 PM

RE: mini challenge: find the smallest cosine of an integer - Albert Chan - 10-21-2021 01:09 PM

RE: mini challenge: find the smallest cosine of an integer - EdS2 - 10-21-2021, 03:04 PM

RE: mini challenge: find the smallest cosine of an integer - EdS2 - 10-23-2021, 06:47 AM

RE: mini challenge: find the smallest cosine of an integer - PeterP - 10-24-2021, 06:56 AM

RE: mini challenge: find the smallest cosine of an integer - Albert Chan - 10-24-2021, 06:17 PM

RE: mini challenge: find the smallest cosine of an integer - Albert Chan - 10-24-2021, 11:42 PM

RE: mini challenge: find the smallest cosine of an integer - PeterP - 10-24-2021, 05:36 PM

RE: mini challenge: find the smallest cosine of an integer - EdS2 - 10-23-2021, 06:53 AM

RE: mini challenge: find the smallest cosine of an integer - Albert Chan - 10-23-2021, 05:10 PM

RE: mini challenge: find the smallest cosine of an integer - EdS2 - 10-24-2021, 08:27 AM

RE: mini challenge: find the smallest cosine of an integer - ijabbott - 10-24-2021, 10:28 AM

RE: mini challenge: find the smallest cosine of an integer - Albert Chan - 10-24-2021, 09:53 PM

RE: mini challenge: find the smallest cosine of an integer - Albert Chan - 10-24-2021, 12:46 PM

RE: mini challenge: find the smallest cosine of an integer - PeterP - 10-24-2021, 06:56 PM

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