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17 events

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Jan 23, 2017 at 15:41	comment	added	usere5225321		@Fedor Petrov. That was my intuition, but i was not sure. thanks for being so patient with me.
Jan 23, 2017 at 15:30	comment	added	Fedor Petrov		If 2 divides $q$, the number of $a$ such that $(a(a+1)(a+2),q)=1$ equals 0, otherwise it equals $q\prod (1-3/p_i)$. The reason is the same as before: there are $p_i-3$ admissible remainders modulo $p_i$.
Jan 23, 2017 at 15:25	comment	added	usere5225321		I see. So how would you calculate it?
Jan 23, 2017 at 15:19	comment	added	Fedor Petrov		If $q$ is divisible by 2, there is no $a$ for which $(a(a+1)(a+2),q)=1$, but the formula $q\prod (1-3/p_i)$ gives a negative value (unless 3 also divides $q$), which is absurd.
Jan 23, 2017 at 13:44	comment	added	usere5225321		Can you give me more details @Fedor Petrov ? I do not see it.
Jan 23, 2017 at 9:49	comment	added	Kevin Buzzard		For what it's worth, the function $F(q)$ and its generalisations came up quite recently on MO at mathoverflow.net/q/259768/1384
Jan 23, 2017 at 6:43	comment	added	Fedor Petrov		Not quite: if $p_i=2$ for some $i$, we have 0. If all $p_i$ are at least 3, yes.
Jan 22, 2017 at 23:56	comment	added	usere5225321		@FedorPetrov Suppose I wanted to calculatee the number of residues $a$ for which $a$,$a+1$ and $a+2$ are coprime with $n$. Does that mean that you would have $q \prod (1-3/p_i)?$
Jan 22, 2017 at 17:41	vote	accept	usere5225321
Jan 22, 2017 at 17:31	comment	added	Fedor Petrov		when we require that both $a$ and $a+1$ are coprime with $q$, the remainders modulo different prime powers are independent by CRT, this is the main feature
Jan 22, 2017 at 17:29	history	edited	Fedor Petrov	CC BY-SA 3.0	added 83 characters in body
Jan 22, 2017 at 17:14	comment	added	usere5225321		@FedorPetrov, thanks for your help. Could you give me more details on how you know $F(q) $ is the number of residues for which $a$ and $a+1$ are coprime with $n$?
Jan 22, 2017 at 17:11	comment	added	Kevin Buzzard		Oh very nice. Relieved to see it agrees with my answer for <= 3 primes :-)
Jan 22, 2017 at 17:00	history	undeleted	Fedor Petrov
Jan 22, 2017 at 17:00	history	edited	Fedor Petrov	CC BY-SA 3.0	added 510 characters in body
Jan 22, 2017 at 16:55	history	deleted	Fedor Petrov		via Vote
Jan 22, 2017 at 16:54	history	answered	Fedor Petrov	CC BY-SA 3.0

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