                           ˿µϣ20091120գ

09.11.20, 츮籨ӷɡ֮Գ
09.11.20, Ƶƿװˮ κȥ
09.11.20, ѧˣǷ浶ǹϳҿζԴ˿ӡ
09.11.20, ˵ƴ󡶴ӺУ׿йƴչء
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09.11.20, һλѧӡԡԺʿרHermiteչ庯ԡһĵ˼
09.11.20, zhongyaojialiuҩơţ˰
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ӷɡ֮Գ

20091120츮籨

 ̷꣩19)գСαѧʿ֮Ƶķӽ籨
ɷʱҲڡһѷֵȻ󣬼ȷѧƣ
Ǽ֮ǳ

źȫ

רҵҲ̫岻˵ʲôҴû˵֮
֪ʲô˼ѧ类ΪXXָ֮ͨĳѧơĳ
ĴߣһѷֵȻ󣬼ȷѧƣַǼ
֪ܵĸסôУǳˡ

ͬѧڿϷģǷѧɹ
оԱΪԼµѧ۵㣬ڽѧۣôӦѭѧ
ύѧģѧڿרҵԱˡۣȡ
רҵԱͬͨý򲻾רҵĹǲ


ڹΥѧ淶ѧٵƵƵкܶо
ͷģѧ뾭øܡ漯໥ĽЩ
ԵľġѧɹǸӦñ־衣

Ԫֵļͱż?ѧԺר

Ĵ-츮籨2009-11-16

ǰһƪԪղ鷢ֵļͱżѧ
߹עгƣйʿѧԺооԱйļͱż
оԱš֮֮ƵĺֽͬڣڹԪִ
ϪӶη˱Ⱥƶϡǵ͵ıżµ֤ݡɴ
Ϊڵļͱż(15)գйѧԺɶɽֺ뻷
оԱľȴԴԲ⣬ͬʱ׫ġײɽܾðαӵġ


򣺹Ԫֱż

Ԫڽղʱڵ˳ĺӹڣ
ӴӲʯϲ˻СǳĶйصԱ϶Ϊ
ż117գֽͬͬйʿѧԺо߼ʦƽ
ʶӵִϪӶʵؿ졣

ӱϪӶϣڽﳤĺӹڵʯͷϣ
˻СܡǳĶũгʯΪ񡣾
ֽͬܣʵձصǡСӴ󡢵ƽżУһ
ҡɽγɵıʽ϶ִ࣬ϪӶεıɱ
γɣڹ״ηֺ֡ͬͳƽһָƵʯͷʾ
СĹ⻷Ϊǵļͱż˵ı־λרжϣ
żγ200ꡪ300ǰ

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ʹ԰ƷƣԴص֪ȡ

⣺ܾðαż

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Ѿ֤й2500µǲڹűżġ

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ľԣΪΪļͱҿȥɽϲ
ɽظԭԭζ顣ĴݹĹɽѩ
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㡰Ƿ塱в˵Ƶġм˲۵ġĥ桱
оǴڱݶɵġ۔۔С米¨
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Ѿ֤й2500µǲڹűżġ

дŸ򡰱ʡЦ

2009-11-19 츮籨

ĴʡЭֱԪξ֡ξֺͱȥ
żԴʮֿ

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ͬĴרѧߵĹ۵㡣

֮ͬľ۵

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֮һʩŷԺʿѾ90䣬Ϊ˲߸Ůʩ
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ԡԺʿרHermiteչ庯ԡһĵ˼

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ıۡķйѧйʶʵйѧȽձ飬
ֵøԶѡЩӿԿѧ

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һΪڸ쵼ߣ̷˼Ǽ򵥵ı⣬
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ҩơţ˰

ߣzhongyaojialiu

H1N1дڴ󱬷Ľ׶Σҩҵ˵ԼҩƷ
ڴƣΪصǣνרҵ
£


ҽѧѧԺ΢воʵ鱨˵ǲԤ
ֲͬĸҩʽΪʹ飬ֱⶨ
ָָڴ1ҡ
ҽҩּH1N1зרίԱίԱ̳ҽԺҽ
ĸⲩʿ˵Ժѡȡ66H1N1лߣֱʹ
ٴ飬ʾƽסԺʱΪ
4.35죬Ϊ4.60죻ƽʱ䣬Ϊ 2.13죬
Ϊ2.80졣ڸʹԡ̵֢״Ժڴ顣

ⶾ
йҽѧԺҩооԱʾҩڴơ
оʾⶾMCDKϸ϶ԼH1N1
вFM1ϸãƣ
ⶾҶԼH1N1вµС
;ԼH1N1вµߵС׵,
ڴ;ߵ״̬,ҩвȾķβ֢
á
ԤҩԺ,вȾԺС,FM1ȾԺҲ
кܺõı,ⶾңԴﵽ78%,СԴﵽ100%,
ʮҩЧ۵Ľкܺġ

ҩơѴΪҩЧıˣҺô
еٴݡйҽѧԺҩооԱⶾ
ĴеͷȻ˵Դﵽ78%,СԴﵽ100%,
ʮҩЧ۵Ľкܺġһҩܹﵽ100%
ֽš

ҹעҩڼ֢Уܹ㷺ӦãЧ
˴գԹۺЧ

ο
http://www.chisa.edu.cn/news/ssxw/kjxw/200908/t20090822_110121.html
http://www.takungpao.com.hk/news/09/11/09/GY-1168897.htm
http://www.ahjiren.com/newsinfo.asp?newsid=125
http://www.yyjjb.com.cn/html/2009-11/05/content_100200.htm

(XYS20091120)

˿(www.xys.org)(xys4.dxiong.com)(www.xysforum.org)(xys2.dropin.org)

¿ȴ۸ҽѧչʷҲ䵱Ժʿ

ߣ

йѧԺԺʿϺҽҩѧУ¿ȵĽ20091119
йҽҩϣΪҽѧδҽѧ򡱡йԤδ
ҽѧķҽ۵£úͳ¿ȡǻῴ˿
³ 

¿˵ҽѧγɺͷչ3׶Σҽѧʱʵҽѧʱ
ҽѧ(ϵͳҽѧ)ʱ ҽڹȥΪй˵ҽƱ
ĥĹףȻҪáѧҽѧչƣע
ֲĲأۺĲأʵĲءʵҽѧʱ
ҽѧʱɵĽ׶Ρ

Ļƽʼ˵ҽѧչҽѧҽѧҽ
ѧڽҽѧ׶Ρ˿200910£
ҽѧĻǣҪһĽˮƽ
ѧĽǶǲģҪ෽Ŭ
磬°ͻȾξͲǵѧܽ⡣

ƽʼҽѧֽչȫ繫ϵġ¿
˵Ĵʵҽѧҽѧʺ͸Ƕ׫ġ¿ȵνҽѧ
ǧǰҽ˺һԭʼ¿Ժʿ֪ѧ
⣬ѧѧѧϸγɹ̺ʵ
ֶΣ¿Ϊ˽ҽѧ׶ֻҪ˵У
ҪʵˣԱҽѧʡ

ҽǸ⽨ɫʵķ⽨С檣Ǹ


(XYS20091120)

˿(www.xys.org)(xys4.dxiong.com)(www.xysforum.org)(xys2.dropin.org)

ΪʲôɽëȺ

ߣȫҫ
blog.sina.com.cn/s/blog_4ac981db0100fyn1.html

ȫļҸ!йԺԺʿ
ڿרɽǰָԼͲĿǰڹٷļ
֣˹ڼýĹ㷺ע

ԴˣëȺڽ籨ߵ绰ɷʱʾ
˵ʾ˵ʵɽ˵Ҳš

һйһָĺרңһϵ˭أ
Ŵһδεν󣬿¶רҡΪʲôأ
ȫҫΪר׷ǿѧĹΡѧʵϣ
ȶһܵĳ黨š

2003ǵ٣רҽ¶԰̲ҩӦԺ
ĸãˡشЦƭֲ
ȵءܱ׼ɲƷױȡƾʲô
š

רҲ󵼵ʱ򣬵ᡣɽëȺ
ëȺɽŷˣǸࣺҧ˭ҧ˭ҧҧڡ

(XYS20091120)

˿(www.xys.org)(xys4.dxiong.com)(www.xysforum.org)(xys2.dropin.org)

--⽡뵽-־

ߣott

꣨1956꣩-໥²غ㡱²ʱΪ
ۼᵽæ˥ƵĲغ㡣⽡1957160
˥ʵ飬֤ʵƲ⡣⽡۵ʵƵ쳣ɣ̹г
-µĽ顣-˵ըҩ⽡ûý
ѧѧ磬λȴ˿ѷըҩʣǵ
⽡ѧϰ־˥ʵ˼·Լԭ͵ըҩ𣿣

ҲѧһţҲ򳬵۵72ըҩ
ӶΪԡҲţɮкףŲ
ѧϰأʤȫۣʲôϵͳʵ
ʤȫ־տţ˼·ʵ֤ʵ˿ţۡ
˵־ĹǺܲģܹʵ֤ʵըҩۣ
ܳʡϧѽϧ־ͷȥţ˵
Լ״־һǵҲΪ⽡ûýλȴ
˿ѷըҩĵˡ

(XYS20091120)

˿(www.xys.org)(xys4.dxiong.com)(www.xysforum.org)(xys2.dropin.org)

ҵĵһƪ

ߣܼ

:Ȥô?

ڹڵѧ٣֮ʱ¶ĳϮ֮Ҳв١
⵹ҲҶµһЩ䣬Ըڴ̸̸ԼľǴմְɡ
Ҳһ¶еһ

һ£֪߲֮࣬ԼҲйصļͼѡ漰ȴ
㣬˵ĵء?ϺʦԺѧѧѧͿѧͨ
߷ֱϺɽһǺϵһλѧʦԷѳһ
СӣҲͬԣͬʱõͬҲһ
̳Ȥ°ɡ

һ£ͬʱ漰λ:޸˳ж˵漰
޸˵һĽҲšң
֣һġ룬һãǹĪɡ
Ǹлġѵͽ֮ӡһӳ
֮ӣȴַһ㳣

˵ܶ˶йľҲֹһΡʵһ
̹ģºܶ˻˵:Ҳˡ˵Ϊֹ
ҲһЩģҪ˵һƪҵһԥ˵:һ
ƪҵĳɴ˿ʼҵѧġ

ĵĳ۵ͯ
Ǵͷ˵һֵй˻ʱѧ֮紵˴أ
󣬳¾ŬĽܣѧʹϵ˶˵
顣ңеһ

ǣ˴ͷ<۵>ͿС鵹ûпе٣еҲ
ú<>ǿгһζˡᵽ:

֪ n2-n+17  0n16 ʱΪ n2-n+41  0n40 ʱ
ΪBeeger:

n2-n+72491  0n11000 ʱΪ˽һȤζ֮⡣θ
һ Nɷһ p
 0nN ʱʹn2-n+ p 

ǻһõ:


n2-n+ p  0nsqrt(p/3) ʱ 0n<p ʱ

Ʃ磬p=72491sqrt(p/3)ԼΪ156Ҳ˵n2-n+ 72491 n156ʱ
Ƴn72490ʱ

ʱȷʵǺ˷ܵġ˵ҰBeegerĽһ֤
n2-n+ 72491 n<72490ʱȻһЩ

ʱ˵ǳ־һƪӣͶ<ѧѧ>

žǻָ߿ܶ൱߿ܻǵãʱ꣬Ҫ
죬ṩ"֤Ĳ"֤ȷʵԱרҵȤس
ʱѳ֮Ϊ""""""֮ʱ泣"
û?"ұһƪĵҵ""ϺʦԺ֪
ԭѧǲôӵġ

ǰĽҵĴʦգǽȷ֤
ѧУʮ졣ϺʦԺУ1958ꡣĸУϲĸ·
Ϊĸ״У죬Ϊʢ¡ʱϵѧ棬ҵ
Уȷ֮ܳСе޷ˡǷġԭҵı
ڴ飬ʱ˵Ǵ̫࣬ҵıƵ̲Ľ̷ȥˡ

ȷô?֤ô?ĳȥĸͬţ뺣дһ
ЩڸӼǡ¼¼:

һ˵ʶʦѧϵʦд͹ȥ
͵˻ʦ
ҺҲĸѧ
¾˸
һֱд뷽æ

õһЩʲô?

ʯġ
Ҳۡ
λͬѧдһƪ£ܲסơ

ǵõʱһλʦרŸ۵ģǵŰݷáʱֵ
٣ðգг龰·ǰǳαŸ
һα"첻Ӵ"ڶȥ˲ڣֽûлӦ
һȥ˵ϿΡ¿ɺãԼˡǵ칫ң
˵ڷֲǸϵֲֲ˵ȥܲٸϵܲܲ˵
ˡյһš

ˣʱҲͽȴˡ

ʦҪȥɽᡣ˵Ҳûһͳ˴˻
Ʒ(˳жʦ?)ʦ˵Ȼ֮áȻ
Ҳûʲô

ҵżңܼҾԺ
ʱ<ϺʦԺѧ>ͶУҵУõϢ
ǣڵһڿǣָˡ

ֵõϢ˵ǲˡΪʲô?ԭ˿Цá
ʱѧıίиϵʦѧϵϵѧϵʦ
ϵһƪӲôͲҪˡѧΪ˸ƽ⣬ʹѧϵҲ
һƪģҵġ

ǵõʱУ԰ϵϵι׳ʱѾˡ
ұѴ¸һֱҹذмӣʱ:"ҪҪȥѧ
к?"ҵʱش:"ˡһӾдһƪģҽ
ȥ˵һ·ءѧʻȥһƪ
ʲôͲ˵ˡ"ʱգԵʱĺ׳̸Ժ

Ҳ֪ûȥǵڶϻǵǳˡ

¡<ѧѧ>ǰĸ˻ҡ˸
Ǿ벻ģȲ˵ԣҲ˵:"ʱѾ뿪ʽԭ
˻ء"ҵȻں

ϵһλʦתһţΪᵽҡ˵:"ͱ
ɡҲûá"ǴűҴˡɽѧ׿дġȫ
:

XX:ã

׿ѧ (60ʦԺѧϵҵ)

82Ʒǰתܼ¡ܱǸһ꣬
пճ鿴һ¡µҪǶԵģ֤δִ⡣ֻ
µĽǰĹͬ־(ϲڹ˾)һĻ
ͬ(ĺһݽϵ־)ԿһǶġ
ͲˡֻýĻء

Ŀǰ˳ж¸ֻۣ弫˲ѣɹأ
һֱӦеССĹҲӦ鹦ָˡͬʱʦԺʦ
ҴµѧҲҪġдˡ

ѧ׿

˵ĻءǲȷģûмиҲûдţ
ۡĻء?⵱ȻʲôҪ£Ҳ⡣Ҷ
⣬ΪҵѾˡ֪бҲ˹Ҳõ
ͬ뷨뽭ϵˡ82귢<
ѧѧ>˵ͬʱ·ϺҴ̽һٷ
˵̸

һ⵽һλѧʦԷѳһСӣҲ
һֻ֤ͷһʱҲⱾСӡӦ˵
˼ͬʱõһҲǿ̳Ȥ°ɡ

ף⺢ôҵĺô
84ʱһλʦң<ѧͨ>һƪºҽơҵȻ
Ȥһ飬ȻƣһҲʶ׿£λ
ҵĸоˡ

Ҹ<ѧͨ>дһšẓ́ܶ˵:

һĽƣ
ҵ·귢
ҵ£Ϊ֤

<ѧͨ>ҵת<ѧͨ>д˻ţ<ѧͨ>
ְתңǶҵĴ𸴰ɡڿ˵֮󣬿϶е:
ô?ǲ֪Ҳ벻һ⡣
ȫ:

ѧͨ༭:

"ڶʽ"һģ˵

161ҾͶԻ޸"۵"ģа"ʽ
"ⷢȤֱ79͵õж123Ƚ1981
3µɽУѧϱժҪʱʦѧԺƷҲ
ڳжм³ȥˡһԺ(82괺)Ʒ
תϺʦԺܼ¡ЩҪʵ༭һ
ʵ

2еҪ֮һ2ֱӴӶ1õģӦ
3òͬķ(12)õġ֤أҪ
ͬ뽭ĽʷҲżʵģΪXX
ԼοͬףõѧԼʵ
Ĳ죬ԽͷȻơ

3еĶ4е6Ҳȫһ4
6شصزģҶĵ¼:
"p,p+2,p+6,...piбΪpi"˽۲ԡΪ

pp+pi(pi-1)(mod pi) p,p+2,p+6,...p+pi (pi-1) piܹ
ģpiȫʣϵ4֤Ȼܳ(֤ãڴ˴
)

6Ǵδ֤4õģҲܳ

ܶ󣬵Ӱڴ˴ԡ

4Ŀ뷽ͬͬҲǶõ
еĶ4ȷ滹ܵĵӰ죬Ҷĸг̴
ȫķϺʦԺҵͬѧ(Ҳʦ)˽
һЩԺҾ;Լһ֣ʱҲ֪
""ϺʦԺ82ڶժҪXXڴϣ
ȷǷףҲ༭鷳ڴǸ⡣ҵĿ׷ָ



ɽѧѧϵ
׿ 19852

ѧͨ༭:

˳жҸд"˵"⣬²˵
("ʽ"һ)

1ϵϺʦԺѧʵڣҲŴӳж֪ܼ
һժҪ(δ֤)ϺʦԺѧ(82)ĵԭ(82괺
Ʒת)ĸҪеĶ46Ǵġ

2ж123߾ǰõֲͬ4
Ӧ6ͬԼԼⲿֽȻǿԵ(Ȼ
ĳЩܵĵһЩӰ)ȷǹ⣬
ʦԺ˽⵽"˺"Լ˵һЩ()Ҳ
ġȷ༭鷳ڴٴαʾǸⲢָ



ɽѧѧϵ
׿ 1985212

е""ԭģĸֿ壬X֮ȷʵȤ
߿ѧͨ༭ʲô?

һĽǶõġʵҴû˵Ϯԣ
Ϊû֤˵ûеõЩ<ϺʦԺѧ>ϣע
1980109յ壬81513յд塣<ѧͨ>ûעյ
øڡô:յҵĸ(˵
82)ҵĸ(˵83)Ȼͨϵһλʦ"
Ͳˡ"ʴ1983113ȻԼȥͶˡ
ʱ䣬84귢áȻҲû֤˵һǿҵĸͶĸ塣
<ѧͨ>ҲĵӰ죬ȻȥͶġ
˳򵹹ڸѧͨ༭ἰĻʵǲ
˼ˡȤ79õȥͶ壬81棬Ҳ
ȥͶ壬83껹ҪȥӰ죬ȻͶ塣߼ôҲ˳ۡ

ڶûд"ԼԼⲿֽȻǿԵ"
˱˵£߱"Ͳˡ"ȻԼȥ
""ô?

ҵº⡣"֤""ܶ"(
Ҳֵ˵£ʵǺܿ)"ĸҪеĶ46
ġ"ˡͲ˵"µҪǶԵģ֤δִ
⡣"˰ɡ̫ѿ߼ͺ֡"4֤Ȼܳ
(֤ãڴ˴)"Ȼ"֤"Ǿ˵ȷģ
Ϊʲô˵Ǵ?"6Ǵδ֤4õģҲܳ"
һǿ֤õ⣬һδ֤⣬һǴ⣬ʵ
ںһ¡

ģȻΪӵ"ϺʦԺ˽⵽"˺"Լ
˵һЩ()Ҳŵġ"·¼ķ
ҸҲ˺£ʶȫҡһ
:ûˣǹ֮û
Ϊ"˺"ԼҸ˵һЩյĽۣβ
ҡ

ҺܻѧҾĵߵڰ׵һ
""־԰ԭͱλûһ""Ϳ԰ѱ˶ҵͬ
ɻɣһ"˺"Ϳ԰ԼƲɾ˵"˺"
Ȼͷ֤õ"ں"˵""Ȼ֤û""
һǴ"ϺʦԺҵͬѧ(Ҳʦ)˽⵽"ģ֤Ǻε
ɵĻԿԶҿһлᣬ
£Ӷ֤Ƕô޹ȫԻɣѾʦ
ǰлᡣܹ֤ģǸš

壬Ҳһ˵£ҲҪ˫ͬ⡣ҵǴûп
ǹ"ں""˺"Ȼûпǹĸ
ΪûбҪҵĸ83꣬ʱҵĸѾһǰ
ˣбҪô?ĽǶ˵"ں""˺
"ʱңҵȻҵѾˡҲ
"Ҳ֪"ĽڡǲǰΪ£ԸⲻԸ֪
ҾͲ֪ˡ

漴Ҹѧͨ༭˳ждһţ˳𡢲⣬
Ҳûյ

Źͬ

棬˵˵һ⡣ҵָУ¼:

ڻ޸<۵>57棬89ҳС

75ٰʱɾȥһ仰

һ"ɾȥ"ĥ˺óʱ䣬Ϊʱһ֪BeegerĽ
ǴġҲ֪Ϊʲôһ仰ҪɾȥӼм¼ŵʱʦĶԻ:

"ڵĽô?Ϊʲôٰвһ?""д
ŸԪⷽĽ"Ƕô֪ⷽĽ
ֻµ˵:"дſ²׵õӦաǷѧУ档"

ἰ:

һŰ0<ѧͨ>ϣ≮°ͺ>һУƷ
ٴBeagerһṩݡn=01211000ʱʽ
n2-n+72491 ֵԱ

ʵϿ:72491=71X1021
52-5+72491=59X1229
62-6+72491=47X1543

һݻڻ޸:<ѧɷ>P7
1964档<>P204-205

ᵽBeagerʵӦΪBeeger֪


72491ڸУͶʱȻѾ֪ˡеʱᵽ
ġУ༭ʱ˵Ȼɾȥˣ˵Ѿ֪ˣ
ͲҪˡһΪ߻˼ɡҲй˵ϰˡʵ
ʷϴѧҽ֤ۡ¶ǣ˭Ҳû˶ʧʲôӡΨ
й˾Ҫǵӡǣʱƺƴоᵽȥ
ʱϢôõˡأƷ0껹֪
á

һ⣬ʵһ⡣֮ΪEuler(Lucky 
Number of Euler)Ķ:һ pʹn2-np p=12 
p-1 ʱѧEuler1772۲쵽41ʡ

ڡѧͨϷn2-npȫȷȷ
n2-npҽp235111741
·1988ꡣע1986յ塣ϧꡣ
1983귨le Lionnais֤Eulerֻ2, 3, 5, 11, 17, and 41 
⣬Ϊ۽һش

ĺӺܶ࣬һģһĺӲ

棬ѧĽǶ˵˵˵Ľ΢רҵһ㣬ѣֻ
Ҫһѧѧ͹ˡҾΪѧȤζѧɡ

¸һ


ʽ
g(n)=n2-n+p (pΪȻ)
n=1,2,...n0=[(-5+sqrt(25+12(p-1)))/6]+2
ʱΪеn=0,1,2,...p-1ʱ g(n)Ϊ
(p=72491ʱ n0=156)

һλѧʦһԷѳСҲƽС
ಿֶѧѧ֪ʶ

ҵ¸g(x)=x2-x),f(x)=x2-x+p)
1һpinpiʱn=Kpi+n1 (0n1p)g(n) g(n1) 
(mod pi).
2(pi+1)/2<n<piʱn=pi+1-n1 (0<n1<(pi+1)/2)g(n) g(n1) 
(mod pi).
1f(n) 0 (mod pi) н⣬1n0 (pi+1)/2ʹf(n0) 
0 (mod pi).
:f(n) 0 (mod pi) 1n (pi+1)/2ʱ޽⣬޽⡣
2n2-n+pnNʱ
f(n) 0(mod pi)pi<min(2N,p)޽⡣
3pjΪ2sqrt(p/3)гȼ:
1f(n)n<pʱ
2f(n) 0(mod pi)pi<p޽⡣
3f(n)n (pj+1)/2ʱ
4f(n) 0(mod pi)pipj޽⡣

3еp=72491ʱ2sqrt(p/3)=310.9pjܴ310(pjj+1)/2
ܴ155ɴ˿ɼĽҵĽǶôӽҲͺһλ
ѧʦĽȽϹΪ˵ĽǶõģʽı﷽ʽ
һǶͬһ֮УԱ˵ĽԺôһ

4f(n)n<pʱ
4p-1Ϊ
5p4,f(n)n<pʱ
ҽ4n2+4p-1n(p-3)/2ʱ
6f(n)n<pʱ
ҽpΪ4p-1֮Сƽʣࡣ

˵67ƽʣ:

1,4,6,9,10,14,15,16,17,19,21,22,23,24,25,26,29,33,35,36,37,39,40,47,49
,54,55,56,59,60,62,64,65

У17Сƽʣࡣ

˵˵ҲǶõġԼһ֡ˡĵȫ
¡

1ΪQ(n)=n2-n+p

Q(n) 0 (mod p)
нĳҪ
p=0,-2,...,-r(r-1),...,-(q2-1)/4 (mod q),
нʱӦp=-r(r-1) (mod q)Ϊ
nr(mod q),
r=1,2,...,(q+1)/2
2plΪС2sqrt(p/3)1n (pl+1)/2ʱ,Q(n)

1np-1
ʱQ(n)
3Q(n)1np-1ʱ
1n (p-3)/2ʱ4(n2+p)-1Ϊ
44p-1Ϊ1np-1ʱ,Q(n) ΪĳҪ
pΪ4p-1ĶʣеС

ҪĺĵͬʵѧҪֻҪʶ
־㹻ˡ

ôרҵˮƽҲֻܿƭ

˵˵֤е""ҵ˵ʱָ壬д
档ôһһ°ɡⲢҪߵѧг̶Ⱦ㹻ˡ

֤:M=4p-1,p,p+2,p+6,...,p+n(n-1)ΪM֮ƽʣࡣ
Ϊ((M-2n+1)/2) 2 =(2p-n) 2 =(4p-1)(p-n)+p+n(n-1)=p+n(n-1) mod M
MΪpi|MMpiƽʣ(xȡȻʱ
ƽM֮ʣ)Ϊߣp,p+2,p+6,...,p+pi (pi-1) p_i
бΪpiߡʱf(x)=x2-x+p

ٸ˵p=174p-1=671719232937pi
332=1087=67X16+17
322=1024=67X15+19
312=961=67X14+23

ɼЩ333231piMͬࡣpiȻ
һΪpiߣӦҲͱΪpiˣҵи
ûõȫʣϵĸɼָ""ҪôڶŤ
۸ûи֤۸ѧͨ༭ƭҪô
ЦȻΪǵݣΪԼˡЦ񲻿ɶ?ҵ
ȷжĵ¼ģĻֻл
һһǲءΪһ(ǳԵ?)
֤ԲŻڶ4"4p-1Ϊ"һ㡣

ʵҵҲһȷᷨӦΪ:

n2-n+pn<pʱ
ҽ4p-1ΪpΪ4p-1֮Сƽʣࡣ

ӣؼҰɡ
Ѿʡ֮ʣ֪׹û?ǻ׹ǻڲ
?ԹҸ"Ϸ"?Ǹлû֮
鷳?

һ̸£˵:"ýҲӦͬʱԷ
ȨԷš"⣬ʵҲҵź֮ڶԷ֮
£ûܸԷȨƺЩֻϲҵ
ԤϡʵҪöȥ񲻱?

Ȼݣǲûһ¡ֱǰ
żȻ֣»ͷƺӦðؼˡ

ʵ˵ûܸԷȨǲȷеġѧͨ
ţô?յ<ѧͨ>תҵ׿ԺҲ
<ѧͨ>˳ͬдšǣǶһšԣҲ
ԷȨûеõȨʱѧܣ
ϮԻûôʢСǶһţʲô취?

Ҳ˽ʷϵһɡʷϣҪ˵ʮǰ
£ǰ»һֱڲ龿ءƪ£˵˵ࡣ
Ҳǰ"ƭ"ĺؼҡֻ֪ã֪⣬̫
˵ΪԷţôҪһֱȥ⣬Ҳ̫


ѾʮˣѧͨǷһ
ϮԣǹƭʲôǣֻǸһӣѧͨҲ
Ӧñһ̬ô˼壬ѧͨӦƳѧѧĴͷߣ
죬ѧͨ룬ѧͨ༭ӦûЩ
żա

ڴˣϺʦԺ""ʱػԮֵĹ׳գ
ȸλʦϺʦԺѧʾԵĸлڵʱڣ
ĴУϺʦԺһܷ硢ĸ塣ǵʱһƪСĲѧ
"Ҹ"Ϊƽ岻
ȥ컹˵ô?

ο
1ܼn2-n+ p ֣̽ϺʦѧԺѧ(Ȼѧ
)19822:35-36
2磬n2-npֲ֣̽ѧѧ(Ȼѧ)
6(1982)17-18
3׿ʽ⣬ѧͨ29(1984)231470
4Shen Minggang, Complete determination for n2-np to be a prime, 
Kexue Tongbao, 33(1988),13:1957-1958.

߱ҵϺʦѧRutgersѧȡòʿѧλжƪѧ
ķڹ־Ž<Թ滮>ɿѧ棬
<Selected Papers on SAS>ɼҳ(BeAuthor.com)档־
 

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ã

˿ʵߣҲķ˿ý嶼ϾͯҽԺҽ
¹ʡŮ15ʱһƪϰշ˳֪Ƿʿ
˿ϣѧΪԼȫҽƱգҽ
ȥ괺죬ҽԺһʹεĿǳݣҽ
ڼ͹ϵĲ𣬲Ϊйܶ

Ĺǵ  
2009-11-20

Ѫ飬ֽҽ

ߣĹ

ҳʱϺüطѪġϡԺԡ
ϣһƤ𺦣Ũͨ¡ѪȺɡеѪ
һ̶ȾֹͣˣȻһССĺ룬Ϊڹ
Ψһ־еѪȴԸͣԼƤĽŲ
ҳʱϵһЩѪǷҵƤ̶һھʹ
֥ô󳤵һӲô󣬶ֺ׵ģʵǺ˵ӡ
豧ȥϾжͯҽԺҽҽ裬ѪҪ䶳Ƶġ
䶳ƾҺҳѪһƤѪҲ
һˡ 

˵ҴԼһµ䶳ơ䶳Ʒ󣬶
ͷϣﻹкĵһЩСѪɹرˣ
һСһİ̺ۣлôСģҲЩ̺
УҸдģǺǸ̺ۣΪǸ̺ۣҺϵ
ǿƤͷ15ǿƤԶǹͺͺġ 

Һ¶180϶ңô¶ȣƤë֯Ҳ
⡣䶳Ƶʲôһָоһ㶼ûм䣬Ϊ
ʱֻǸ´СӤ˵ÿȥƵʱû
ԼҽңðְֱȥƣԼվ棬Ҳ
һۡÿÿǺ޿κΣܻ̲ס
Ҫᣬ˵Һ䰡ƶҩǶС۵㶼
ϣҽҪģѧʱûѧҽ 

룬ô¶ȣתƵʱʲôоô¶ȣ
ǿëҶʱֵжô䣿 

䶳֮󣬳ϵһѪ⣬Ѫ
Ⱥˣֻһǿô˳ű
ǿƤıԵٴȥΣƤѾһƬСɽ
Ƭô󣬶ƺûҪֹͣơ

һ죬䶳׼ؼʱһһҩСʿס裬
Ҫٴ䶳ˣȥҲԶõģǵϾƤ
ȥһѪķûʹġְֱ
ҵƤǸʹ֮Ǹ޴󡱵Ѫ
漣ĺˣһͭǮô䶳µ˰̣Ǹ
չһ㡣˵ܾͻӰˣܴˡ

ǵö֮ڻϼҹĹϣһԷԼǳ
ûµĶӡǴϾģǸСкҲѪ
Է˵ϾͯҽԺ䶳˺óʱҲʲôЧۿѪѾ
аôˡҽһҧ˵䶳ûİ취¹ˣֻ
ϼҹϾ䶳ְ̰ƤƷܸ
ǶԷ򸾣˵߸̾ҵܵĿࡣ 

 

ְ趼˵ҲΪСʱԸӲԵʣҵһ
ŵüңְ˵10ʱҽƣʱ
룬֮ݻȻһ£ȥŵ롱Ŀȥ棨
08ȥҽʱҽ˵ݾҲ˵
ҽΪûãͬʱҲһ⣺֮Ϊ
ҧλȫıˣؽڴλһ𣬳Ūѡҽ
˵֢ƽˮһͻỺ⣬ʵڲҪ롣 

Ҳ֪ôججضɹ˽5ʱ䣬ֻ֪ĳһ
糿ѹҵһҲŲˡȥǻרҽԺĵһר
˵Ļҽ˵ĴͬС죬Ҳʲô֢ƽˮһͻ
ˣʵڲٴ롣ȻҿһڵֹʹҪˡ
ĵڶרƺ΢еˮƽһXƬȻһۣ
˵ؽڵĹͷѾˣȻҵӲ˰죬˵ˣ
ؽҸˡʵʱҵĹؽڸûд򿪣ֻǸӲͳ
΢һ㣬ʹ̣רһҧǴˣȫҵĸо 

 

12ʱ̿ʼ岻ûƶѪסϵ
СϣϾҽԺҽˮƽߣ͵ϾרҼ˼Σ
˹ȶûʲôҽһֱƶѪƣƶѪһֱβá
߶˵үүӪֲֳԲѪҩû⣬Ϊʲôƶ
Ѫβãֲ鲻⣿רҽûиļֶΣÿο겡ҽ
ЩƶѪҩ̵̣Ĳʱʱá3̵֮ˣ
ϵҽԺβ׺Ͼ׼ȵְֵλ
ҽԺB飬ȴ̵ĸࡢȶ˰飬޻֮
ˣȫ˳ڱʹСǽ1º̾ˡº֪
õǽ᳦˵֪ĻһƵİֻ֢Ҫ
ǶγӼͿˡô򵥵һΪʲôڴСС
ôμоûбأ֮ȴβףƶѪһ
еĲ̱ȷǽ᳦ʱҽ˵Ի£Ȼ
һ¶ûлΪʲôΪҽԺΪĲȡƼÿ
Ԫһ֧ĵ룬ʹϸõԴԴϵӪѸɢ 
 

ҹӵ˾˵ĵ绰˵⹫ŻбΪлũ
ҩ˶ʳж͵ҽԺȥˡΪֹѾһʱ
ˣ⹫ɻԲѣ֪ܲܰһءϻϼңҽԺ
ûи⹫Żбô£ϴθҲ˵Щ綾ʳӦû
ǵĶҽʳжѣֻǸ
֣ҩˣ¡ϴθк೦Щ򵥡
ЧҲҪķȴһûáЩͨѧϰѡζΪҽ
ˣѵô 豾Ͷҽ⹫ѹҲ
ˡ 

Ҷ˵ҽǰʹȴҪ˵ҽѪ
ˡѪ飬ֽҽ

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ııɺɵ

ߣ̷

ⳡϱҽƾ׵ۣǾˡ¹
ĶԣʵڲۡȻλҾ˵䡣

ȫ˴ί׼ҽġ֤εáʱ
ӾƵͻȻϱҽƾװӽϾҽƾװһ֪
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ڶԿ롣һֱΪϰֻĽû뵽ӾƵֲ
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ġҰĺ͵Ҷӱһ֪⣬ǲġӵƵ
ͽĿܶ࣬ÿƵͽĿĲΧȷֹҲĻ
ỹҪֹʲôҽԺҪҽֿƸʲôۿҽ԰
ҽԿڿƼôִҵҽʦҽԺҽʦִҵΧ涨
ѵӶԸרҵƵûڲ涨ôҲ´ˣС֮ĶȾ
֮ΪԶԶ˴ķΧ

ھ֤εǷʵǰ׾ġطԾ֤εá
ùˣ۵û䡣ȫ˴ΪʲôҪۣý
Ѿ͸¶ܻᱻϳ˵ƹ۵˲ֹһֻһ
ֻ߽ҽƽԸȫ˴ίỹҪԴ
ۡΪȫ˴ί᲻ҽƽ˴ίᣬΪҽƽ
ķԶһɵ˾רۡ

ڷϳ֤εúҽ֮ĹϵкתǶ񻯣
һ£ҲûԸı䡰֤εá˾ͱκλ롣ʹ
ϳˣճ͹ԣҹҽǲȡҽƵ̬
һʱڣҽìҲΪһ˾͵ı仯Եĸı䡣
Ψһıģһҽƹ˾ʦҪҵʽת䡣ǰҪҽ
Ժṩ֤ݡ֤ԺҪʦǻŬذﻼռҽƹ
ҽĹʧٱǰҪרҵ֪ʶһĳЩ
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Χ˺ԼԴ˲ʲôϣҽƽҲΪ˻Ĺ裬Ҿ
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ҽˣ֤εõ˾͵ı仯ҲˡΪʲôˣ
ֵúܶ˼һ¡

ǰҪ⣬һǡ⣬ǰ참ʽ⡣
֪ǰλôԲ˵̬ȵȥˡҽƾװ
ʵڲ˵Ϊܶʵಢûиǰ漰ҽָ
ûԳƹǿרҵվһ£ҲۣΪǸС
Ǹ͹۴ڣֻһУеҽѧԺУҽ
ԺͽѧҽԺСȻɹ涨ˡ⣬ûпɲԡ
£ѡԽҪоͽʵ
ϰӻǺġҽƾȥλڣ
Ҳ˵ҽĶ֪дС޸ߵ͡ƤС
ǻ̶˵ģѵλڲ֪ҵĲ뵹ǣԼҽԺ
ҽԺ쵼ҽʿӣ˱ȽϷģˡзա
һ򵥹ˣΪҽԺСǱǰô

Ĺ涨ûʲôʵϵĲͬʵʩϸʵ
ʮǧΪҪٴйصĿУٴPhD
ͨҽʦִҵʸԡҹܶ౾ӦҵԿٴ
רҵоûִҵʸ񣬵ٴֲòӴˡͲ
ìܣĲҲͲһˡڶڼ䣬
ִҵҽʦʸԡŽѧҽԺܶνٴо
⡣

ٴޣԷȰһʱִҵʸ񡣶
ǹҹ涨ڽ޵λڵִҵʸⲻƶϵȱ
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ֵļһֻ˼ҼȥͿչ
Ƿĵҽ￴𣿸ҽԺͽѧҽԺ˲ŵĻ
⣬ǻݼǧ򻧵顣ҽĽʱһһ꣬ұ
ִҵصġһҪ2ʱ䣨˴кϣ
㣩ʡаʱʹ̵4㣬ҲԲʵ
ʡѵҪ4²ԲȲ

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۵㣬ΪΧ֯вأΧ֯׿Ǹ
󣬸ԭ­ڸȾ߰Ѫ֢Χ֯
ڼѹ­ڸȾѪ֢ΪʲôҪ⣿Ϊ漰
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ϷģλҪ¿ѭѵĸλ涨ϰڼϷ


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صֶΡıĳɡֶΡΪʲôҪģҲС
֮ĶȾֶ֮ڶôձ飬ΥġΪ
ǵԸ֣ͲΪΥΪ̷283Ƿ
յרüĵģͽ̡ۻ߹ơԸ
Ҳˣ졢ݵϣΥʲ
ôνĵУƶİ참ֽ
ֵذ˵ƶܺãΪʲôҪķϳأʵ
ǰƶҲǸԩٴƶĽΣ΢˽
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ҲûйϵǿıҽԺһЩдıһ¡
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ëĳڶȻʱ򣬰˵绰ؿ
ҽȡߵı򵥵кü汾ϣҶ࿴
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صĹ磬𱯾硣ǿѹ£ĳλί
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ˡ

Ǽλҽ̸Ҳ̸һ⣬λݵڿƽ
ǵ󣬾úܲ˼顣ڰеλëĳ׾ʹõ
ְ»Կ±ȴʹõġҽ¹ʡҪ
صöࡣëĳְ֮ϵĻëҽ
Ӵ̷335ҽԱزΣɾ
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һͿĲʡǱҵһ֮

Σ Թҽ̧ˡԡĴ죬ƺǴƵġΪ
áԡĿںźøһЩԹҽCCTV顣ҿ
ҽԼ̨CCTV)ŪһˮƽʵԸԭ
򵥣󲿷ֵĵӽĿ޷ǾִڣĿиַ׼ȷ˴;
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Ҳ֪ʵЩҪĵӽĿҪǺϸģ
ʱ˵һҪ50Ԫġھ˵ǵ200Ԫˣ

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ӦϽ̬ȾͿġΪȻϵҲдʱ
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дڣдʱ䣨1010AMڻʿǩд
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УȻô᲻֪е봵ڣϺ
ִʽִ۴йǸأѣϺ
λ˾ָϵģ

ĿǰĲҽԣ£ҽѲ뷨
ʣȴšԡԸڵµ˼ΪʵеԾ
˼Դĸе

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챦¼ǱȻ

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ټ

1֪ϾһҰԺ¥ҽԺϾһ
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һλСҽʦӵҽԱ߻һŮ֡
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顣λҽʦ˵ֲƤһûΣҪת
ƤȥԺʮ־ȣְҽֺľ˵һ顣֪
ûȥǼҪתƤȥֻȥƤơƤƺ
ҵĽֺĹ̺λơҽʦĸ߼˵һ顣λҽ
Ц

220059µһͻಡ7ʱ¥ҽԺҿ
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ǵ˺ܳʱ䶼ûλҽҲΪҴ绰ֱ9
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320064ͷ衢ѣס˹¥ҽԺҽòɫBҼ
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ҽ벡ˣ

ߣDW

ҽٻˣĮĸоʵҲԲ˼˵
һ£ҽ˵һСʱʱһֱڵ״̬ҽ
˼һһֱšͿܳҽǰ
̫ಡ˼false alarms,ġ

¹ʵҪԭҽҲвͬĿ
ΪǿԱģҽ˵ͳܻһļʡ
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