Message-ID:

6 May, 2024: The networking issue during the past two days has been identified and may be fixed. Will keep monitoring.

interests / rec.puzzles / Re: for prime p, ( p ^ 4 + 14 ) is not prime.

Re: for prime p, ( p ^ 4 + 14 ) is not prime.

<t8oeiv$634$1@gioia.aioe.org>

https://www.novabbs.com/interests/article-flat.php?id=183&group=rec.puzzles#183

Path: i2pn2.org!i2pn.org!aioe.org!SABVAYcHOklaNK/u1FQzwA.user.46.165.242.75.POSTED!not-for-mail
From: emurph...@zoho.com (Edward Murphy)
Newsgroups: rec.puzzles
Subject: Re: for prime p, ( p ^ 4 + 14 ) is not prime.
Date: Sun, 19 Jun 2022 17:21:44 -0700
Organization: Aioe.org NNTP Server
Message-ID: <t8oeiv$634$1@gioia.aioe.org>
References: <db0320d1-1b03-4c8e-a367-1eebae6c4657n@googlegroups.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Info: gioia.aioe.org; logging-data="6244"; posting-host="SABVAYcHOklaNK/u1FQzwA.user.gioia.aioe.org"; mail-complaints-to="abuse@aioe.org";
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
Thunderbird/91.10.0
Content-Language: en-US
X-Notice: Filtered by postfilter v. 0.9.2

by: Edward Murphy - Mon, 20 Jun 2022 00:21 UTC

On 6/17/2022 12:13 AM, henh...@gmail.com wrote:

> Show that
> where p is a prime number ,
> ( p ^ 4 + 14 ) is not prime.
>
>
> (sorry if this too easy)
>
> pls wait at least 1 week posting answer(s) or hints.

Rather than waiting (and possibly forgetting to post at all), the usual
methods are spoiler space or rot13. I'll use both.

c = 5 -> c^4 + 14 = 639 juvpu vf pbzcbfvgr (3 * 3 * 71).

Nal bgure cevzr c pna or rkcerffrq nf 5k + l, jurer
k vf n aba-artngvir vagrtre
l vf bar bs (1, 2, 3, 4)
Gura jr unir
c^4 + 14 = (5k + l)^4 + 14
= 625k^4 + 125(k^3)l + 25(k^2)(l^2) + 5k(l^3) + l^4 + 14
juvpu vf pbzcbfvgr (5m sbe fbzr vagrtre m > 1):
Gur svefg sbhe grezf ner aba-artngvir zhygvcyrf bs 5.
1^4 + 14 = 15 = 5 * 3
2^4 + 14 = 30 = 5 * 6
3^4 + 14 = 95 = 5 * 19
4^4 + 14 = 270 = 5 * 54

Subject	Author
Re: for prime p, ( p ^ 4 + 14 ) is not prime.	Edward Murphy