Timeline for Compute polynomial $p(x)$ if $x^5=1,\, x\neq 1$ [reducing mod $\textit{simpler}$ multiples]

Current License: CC BY-SA 4.0

35 events

when toggle format	what		by	license	comment
Jan 12, 2022 at 14:33	history	reopened	Bill Dubuque polynomials
Jan 12, 2022 at 7:05	history	closed	Jyrki Lahtonen polynomials		Duplicate of Gre Question Complex Number (plug and chug) [duplicate]
Jan 10, 2022 at 8:52	history	edited	Bill Dubuque	CC BY-SA 4.0	edited title
May 15, 2020 at 19:07	history	edited	Bill Dubuque		edited tags
Nov 24, 2019 at 19:47	history	edited	Bill Dubuque	CC BY-SA 4.0	edited title
Jul 8, 2019 at 13:31	history	edited	nonuser		edited tags
Jun 10, 2019 at 0:01	history	tweeted			twitter.com/StackMath/status/1137872269076836352
Jun 6, 2019 at 20:23	audit	First posts
Jun 6, 2019 at 20:23
May 24, 2019 at 17:50	audit	First posts
May 24, 2019 at 17:50
May 17, 2019 at 9:10	comment	added	Henrik Erlandsson		All methods that have been taught as part of the course are eligible for test questions, period. If the teacher blundered, a top student may bring it up; the rest will feel bad for not knowing what they shouldn't. Thing is, a top student couldn't solve this if he wasn't taught it. With the comments from college students and PhDs here, it seems bounceback's answer addresses the question closest, most seem to just solve the problem which is not what your question is about, as I read it.
May 17, 2019 at 6:25	audit	First posts
May 17, 2019 at 6:26
May 16, 2019 at 16:35	comment	added	PersonX		What kind of test? Is this part of a math competition, or a classroom precalculus exam?
May 16, 2019 at 14:39	history	edited	Bill Dubuque		edited tags
May 16, 2019 at 13:49	comment	added	Bill Dubuque		I added some explicit examples to the end of my answer to emphasize the ubiquity of that simple idea.
May 16, 2019 at 8:49	history	edited	joeblack	CC BY-SA 4.0	deleted 252 characters in body
May 16, 2019 at 8:48	vote	accept	joeblack
May 15, 2019 at 21:06	comment	added	LarsH		I'm probably missing something, but... The above trick seems to show that when $Q(x) = 0$, $P(x) = Q(x)$. But (a) the original question didn't specify that $Q(x) = 0$; how do we know that the answer $P(x)\equiv\mathbf0\pmod{Q(x)}$ applies to other cases? and (b) the original question asks, "what is the remainder of $𝑃(𝑥)$ divided by $𝑄(𝑥)$?" but the answer given here says let $Q(x) = 0$; doesn't that mean that the remainder is not defined? en.wikipedia.org/wiki/Remainder#Polynomial_division
May 14, 2019 at 23:33	comment	added	Mark		My approach would be to observe that the exponents on P(x) look like they're set up to produce an elegant answer. The common elegant answers are "1" and "0". Since the "+1"s on the polynomials are clearly intended to cancel out, the answer must be "0".
May 14, 2019 at 17:35	history	edited	nonuser		edited tags
May 14, 2019 at 15:48	comment	added	logarithm		One observation is that in that question the step of 'multiplying both sides by $x-1$' is only presentation and doesn't really represent any advantage for solving the problem. What is really important is observing that the roots of $Q$ are the fifths roots of $1$ besides $1$, or that is a factor of $x^5-1$. There are many ways to compute this remainder that are simple to do in a short time. So, don't include that 'multiplying by $x-1$' as part of what was required for the students to solve the problem
May 14, 2019 at 6:59	history	edited	joeblack	CC BY-SA 4.0	added 252 characters in body
May 14, 2019 at 6:52	vote	accept	joeblack
May 14, 2019 at 6:55
May 14, 2019 at 3:54	answer	added	Hari Shankar		timeline score: 23
S May 14, 2019 at 0:26	history	suggested	ReinstateMonica3167040	CC BY-SA 4.0	improved formatting
May 13, 2019 at 23:56	review	Suggested edits
S May 14, 2019 at 0:26
May 13, 2019 at 23:34	answer	added	Henry		timeline score: 10
May 13, 2019 at 21:24	answer	added	Sam Benner		timeline score: 12
May 13, 2019 at 20:23	history	became hot network question
May 13, 2019 at 19:07	answer	added	nonuser		timeline score: 46
May 13, 2019 at 19:05	answer	added	Nightgap		timeline score: 4
May 13, 2019 at 19:03	history	edited	Bernard	CC BY-SA 4.0	edited title
May 13, 2019 at 18:58	answer	added	DanLewis3264		timeline score: 30
May 13, 2019 at 18:49	answer	added	Bill Dubuque		timeline score: 56
May 13, 2019 at 18:46	history	edited	joeblack	CC BY-SA 4.0	deleted 1 character in body
May 13, 2019 at 18:38	history	asked	joeblack	CC BY-SA 4.0

toggle format