(2n-3)(2n-1)(2n+1)(2n+3)=1 (mod8)
1*3*5*........=1*3*1^12=3
125,375,625,875Τmod8=3ˤʤΤ
98ڡ 0:06:31 45152
̤ꤹ1
Фϡ
Ƕ񤭹߾ʤǤ͡
񡡡 98ڡ 0:12:33 45153
ߤ
ȤƤΣ򣳲ʾ夫ƤΤǡܿˤʤΤ餫
δܤ顢ϣΤɤ줫
ʾ狼ʤäΤǡĤǧںǤ
98ڡ 0:43:45 45154
鯤ο
ϡ׻ФǤ뤬#45152Ķ̲פĤʤ¤ꡢ񤭹ʤʷϵ4ĤΤΤɤ줫˹ʤΤˤɤ褦ȻפäƤޤ˥ޡȤʲǤ񤷤
98ڡ 0:50:04 45155
٥륯åĥ
ˡפĤʤäΤǡ¿פƴĥäɮƤߤޤ
98ڡ 0:54:15 45156
ǯ
ͣӡݣţأãţ̤ǰȯ
ʤƴǤ礸ʤƺä
98ڡ 1:23:33 45157
ϥ饮㡼ƥ
Ϥ褦ޤ

10BASICǤ줫黻Ū˲򤤤Ƥߤޤ
98ڡ 3:16:00 HomePage:湩ؤ˥45158
ϥ饮㡼ƥ
֤ˤƤäƵΤֻŪȻפޤ
98ڡ 3:48:02 HomePage:湩ؤ˥45159

Фϡ
κä굯ƤΤɤʤޤ
13579ΤΤ˶ڤäƤȤƤ⹩פȤϸƤ٤ʤήǷ׻Ƥߤ顢
5152535455565758595βƱˤʤ褦Ǥ
鲿äƴǤ
ɤɮ̵Фޤ

98ڡ 4:47:20 45160

Ū狼ޤ
ΰ̡ʣĤΤǣˤäƣʳDZƶΤϣ
ᣱᣳᣵ᣷ȣܤƤⲼϣܤѤʤΤ
β夬狼⤽Ʊ
ǣᣱβ壸ˣȽ˳ݤƲ򸫤ȣ򷫤֤ƤƣݤȤ
ʷ׻ϤʤEXCELäƤη׻Ǥ
ʥޥޤȤäƱǤ͡
Ϻꡡ 98ڡ 6:47:01 45161
(Keigei)
ܿ򣳸İʾݤΤ 125ܿ
dzä;˴ؤƤ (1357)^12(13) 򣸤dzäơ1^1233
125ܿǣdzäƣ;ΤΤ 1000꾮Τ 875Ǥ
98ڡ 7:48:06 45162
vbscript
a=1:j=3
do
a=(a*j) mod 1000
j=j+2
loop while j<=100
msgbox a
98ڡ 8:19:56 45163
ǯ
é夤Ȥϡ#45152¾¿ȰǤ
ƳݤX3aȤȡX125*8*na
X5, 25, 125, 625,, 5^10ܿǤɬפꡢa125*b
1, 3, 5, 7, 9, 11, 13, 15 ,17 ,19,.γơ8dzȡ;ϡ1, 3, 5, 7, 1, 3, 5, 7,ġ
1*3*5*78dzä;ϡ1ʤΤǡ1, 3, 7, 1פ4Ĥ򷫤֤199ޤǤ8dzä;3
125*b8dzä;꤬3ʤΤb=7a=125*7=875
ޤǤǤ
98ڡ 10:24:35 45164
Sueh
Euler1*3*5*71 mod8ˤ
;1000=8*125
98ڡ 10:42:22 45165
cocogoo
3x94510
98ڡ 10:46:13 45166
ˤ
ФȻפޤ
255125
ޤ13578ܿ1
13ߡ998ܿ111󤫤ơޤ8ܿ18ܿ3
8ܿ58ܿ78ܿ18ܿ3򤫤롣
258ܿ1
58ܿ5
Ϥ2Ĥ
125(8ܿ1)(8ܿ3)(8ܿ7)
(8ܿ1)(8ܿ3)
125(8ܿ7)
3875

98ڡ 11:07:00 45167
dyslexia
ʤͭ̾ʤǤ͡
㤨 2009ǯܥ˥إԥåͽȤ
𻳤ϼ 98ڡ 11:14:01 45168
dyslexia
Ǥ
3 50Ĥݤ碌Ѥ 1000dzä;ʤΤ
1000= 8125 ȹͤ 8dzä;Ĵ٤Ƥ Ǥ
𻳤ϼ 98ڡ 11:35:31 45169
uchinyan
Ϥˤϡơϡ
ϡĿŪˤϴñǤƱʤɤΤäƤ;ܤ䤹ä餫Τޤ
Ǥʤȷ׻ιפǴĥ뤳ȤˤʤޤʤʤѤȻפޤ
äȤ⡤Ǥ̵ǤȤƤϡץϤǤ⥳ĥķ׻С
Ūưפ˲򤱤ƤޤΤǡñȤΤʤɸŪסʤΤΤޤ͡
βˡϤʴ

Ȥ 1000 dzä;ΤȤʤΤǡ1000 = 8 * 125 ꡤ 8 125 dzä;ܤޤ
ޤ125 dzä;ϡݤ 5 25 ޤΤ 0 ǡοƲ 125 ܿǤ
ǡϡѤΤǤϤʤΤǡ125375625875Τ줫Ǥ
8 dzä;ϡ
γݤγƴ 1, 3, 5, 7, 9, 11, 13, 15, ..., 89, 91, 93, 95, 97, 99 8 dzä;Ѥǡ
ϡ1, 3, 5, 7 12 󷫤֤ 1, 3 Ѥǡ1, 3, 5, 7 Ѥ 8 dzä; 1 ʤΤǡ3 Ǥ
ǡ 8 dzä; 3 Ǥ
ۤɤΣĤθΤΤ 875 ʤΤǡ 875 ʤޤ
98ڡ 12:19:24 45171
⡼ޥ
ߤʤΤ褦˵Ť^^;;
(50-1)(50+1)(50-3)(50+3)(50-49)(50+49)
=(2500-1^2)(2500-3^2)(2500-49^2)
25C0-25C1+25C2-25C3+-25C25=(1-1)^25=0

soIJ...
500-1^2*3^2**49^2
=500-9^5*5^10*9^5*1^55^10δ...
=500-9^10*5^10
=500-5^10
=500-625
=875
ߤʤȤǡ^^;
98ڡ 13:29:04 45172
uchinyan
ǼĤɤߤޤ


ʲεҤϡ⤽ϻ伫ȤٶΥ˲᤮ʤΤǤ
޳ѤʤΤǤͤޤǤˤȻפäƸΤǤ
Ȥ⤢äơˡʬϻ F.A.Q. ΡֻϰϡפεҤ򻲹ͤˡ
ĿͤǤиǼŪ˹ԤäƤΤǤäơҴŪʤΤǤϤޤ
ޤǤ⤴ͤǤ餺

#45152#45154#45155#45162#45164#45165#45167#45169#45171#45174#45181
1000 = 8 * 125 8 125 dzä;ܤƲ򤯲ˡ
125 ܿܤΤ⤢ޤޤǤäʬषޤ
˳ͥǡβˡ¿Ǥ͡

#45156#45159#45160#45161#45166#45172#45175#45183#45189
׻λפƴĥˡ
¤Ϥ褯ʬʤˡ¿ΤǤʹפ򤤤Ǥ

#45179
25 ޤǤϴĥäƳݤ򤷤ʹߤϵ§򸫤ĤƲ򤯲ˡ
ϡ#4515ʤɤη׻ιפΰǤ
طʤ#45152ʤɤ;ռͤΤǡʬˤޤ
Τˤʤоˤʬ䤹⡣
äȤ⡤ˤ;򤦤ޤȤ褦ˤʤ줿餤Ǥ͡

#45157#45158#45163#45184#45191
ץˤˡ
911 11:47:05 45173
2N.K.
ˤϡ
ʺ?ʡˤϿƤޤޤ

ФǤ礦
8dzä;꤬1,3,7,1η֤ʤΤǡ
μΤޤ3ĭ

ޤ餫ˤμ125ܿʤΤǡ3125,375,625,875ĭΤɤ줫

μη׻̤????ġ????ABCȤ롣
????ġ????1000ABC????ġ????1258ABC
Ȥɽ롣

ˡꤳμ8dz3;ΤǡABC8dz3;Ȥ狼

äơΤ8dz3;875Ȥʤ


ۼ֡ 98ڡ 16:55:38 45174
ˤ⡼
ФϡǶ籫³ơ
ܤ彣̤̳ƻΤȤۤǤ

ƺǤγѤǤϤʤ
#45172ͤΤ褦ˡa+b(a-b)Ѥơη׻򤷤ޤ

轵37Фˤʤ륢եǤǾȥƸͤơǤλȿؤ꽸ʤĶعˤ㤤ޤ
ʡ㤤פȹԤɤǽ뤳Ȥܤ˸ƤΤǡ
򤤤ơǤǾλӤȤΤǤ
󡢻轵ĩ路ƤޤΤǡȤꤤפޤ

޻Ա¶ʼΡˡ 98ڡ 21:27:15 45175
2N.K.
褯顢ͤβˡ#45174#45171uchinyanȤۤܡ˰Ǥ͡
ۼ֡ 98ڡ 21:50:22 45176
M2-N.K.-
ɤǤ⤤Ǥ⤦2شֿפȤΤϤʡȤפΤǡѤޤ
ɤǤ⤤Ǥ͡狼ޤ

˿ع 98ڡ 21:56:01 45177
̤ꤹ1
ɤ͡
ƥᥧä׸ͥǤʤä줧
ɤƤ󤸤㤳ΥХ쥧()
񡡡 98ڡ 22:17:41 45178

modȤ鷺ˡäݤǤʤͤƲ򤤤Ƥߤޤ

ϤŤDz3η׻򷫤֤7111310011ʤΤǡ3ĤοϽ

25򤫤675ˤʤꡢθϡ875375625625פ4Ĥο۴Ĥ롣äƵ§顢875

ˤǽñʤ륵ʤΤǡ
(a)ʤ25򤫤夫۴ĤΤ
(b)ʤ4Ĥον۴ĤˤʤΤͤޤ

(a)5ܿϾ礫5, 15, 25ǡ25򤫤Ȥϡ
55551255675δܤˤʤ롪
(b)12581000ʤΤǡ
ʤ8ܿˤĤޤꡢʤ8dzä;ˤ򤫤ƤФΤǡ
67527(1255)3125151257=875
87529(1257)5125351253375
37531(1253)7125211255625
62533(1255)11255625
ʲƱ͡äơ4Ĥον۴Ĥ롣

998dzä;3ʤΤǡ˳ä875
ʾ塢ޤ٥ι⤯ʤ(ǯ)Ǥ
98ڡ 22:57:39 45179

675ǤϤʤ625Ǥޤ󡣺ˡ狼餺
98ڡ 23:21:09 45180
ޥ
ǤƵ٤ߤνȤȤǡ˿عǽꤵƤΤҼڤޤʤȡ˥ΤäΤǤ...

ϡ֣̤˹ʤפޤǤϤʬäΤǤθιʤߤ˻֤ޤɤmod 8ˤʤޤ
iMac 99ʶ 9:11:33 HomePage:45181

99ʶ 10:47:16 45182
uchinyan
ϡ 125 dzä; 8 dzä;ǹͤ롤åꤷƤǤ⤢褦Ǥ
ߤ˷礱Τǡ⡤׻ιפǴĥ롤Ȥˡ˥ȥ饤Ƥߤޤ
̤Ȥơ#45160#45161#45166դƸˤʤä褦Ǥ
ʲη׻Ǥϡ̤򳰤׻ƱʤɤȤäƤΤǡ
ΤޤޤǤϻǤϤʤؤǤ׻Υƥ˥åɽδˡʤΤǡ
ǤϻˤʤȻפޤ
ʲǤϡ
ʤΤǡƱ֢פ mod 10001000 ̵ܿ뤷 1000 dzä;֤롤Ȥ
100 ʲδѤ P Ȥޤǫ˽񤭤ޤ

ޤ
1 * 3 * 5 * 7 * 9 = (1 * 3 * 7 * 9) * 5 = 189 * 5 = 945
11 * 13 * 15 * 17 * 19
= (10 + 1)(10 + 9) * (10 + 3)(10 + 7) * 15
= (10 * 10 + 10(1 + 1 * 9) + 9)(10 * 10 + 10(3 + 7) + 3 * 7) * 15
= (200 + 9)(200 + 21) * 15 = (200 * 200 + 200(9 + 21) + 9 * 21) * 15
= (40000 + 6000 + 189) * 15 189 * 15 = 945 * 3
21 * 23 * 25 * 27 * 29
= (20 + 1)(20 + 9) * (20 + 3)(20 + 7) * 25
= (20 * 20 + 20(1 + 1 * 9) + 9)(20 * 20 + 20(3 + 7) + 3 * 7) * 25
= (600 + 9)(600 + 21) * 25 = (600 * 600 + 600(9 + 21) + 9 * 21) * 25
= (360000 + 18000 + 189) * 25 189 * 25 = 945 * 5
ʲƱͤˡ
31 * 33 * 35 * 37 * 39 189 * 35 = 945 * 7

81 * 83 * 85 * 87 * 89 189 * 85 = 945 * 17
91 * 93 * 95 * 97 * 99 189 * 95 = 945 * 19
ǡ
P = 1 * 3 * 5 * 7 * 9 * 11 * 13 * 15 * 17 * 19 * * 91 * 93 * 95 * 97 * 99
945 * (945 * 3) * (945 * 5) * (945 * 7) * * (945 * 17) * (945 * 19)
Ǥ

ǡ945 = 1000 - 55֤С#45160#45161ǡ
P (-55) * ((-55) * 3) * ((-55) * 5) * ((-55) * 7) * * ((-55) * 17) * ((-55) * 19)
= 55 * (55 * 3) * (55 * 5) * (55 * 7) * * (55 * 17) * (55 * 19)
= 11^10 * 5 * 15 * 25 * 35 * * 85 * 95
11^2 = 12111^3 33111^4 64111^5 05111^6 56111^7 17111^8 88111^9 69111^10 601ꡤ
601 * 5 * 15 * 25 * 35 * * 85 * 95
5 * 15 * 25 * 35 * * 85 * 95
θϤǤޤ㤨С޳ѤʤΤǰη̤Ȥȡ
= 5^10 * 1 * 3 * 5 * 7 * 9 * 11 * 13 * 15 * 17 * 19
ȤƤơ
1 * 3 * 5 * 7 * 9 * 11 * 13 * 15 * 17 * 19
945 * (945 * 3)
(-55) * ((-55) * 3)
= 55 * (55 * 3)
= 55^2 * 3
= 3025 * 3
25 * 3
P 5^10 * 25 * 3 = 5^8 * 625 * 3 5^7 * 125 * 3 = 5^6 * 625 * 3 5^4 * 625 * 3
5^2 * 625 * 3 625 * 3 = 1875 875
ĤޤꡤP β 875 Ǥ

ۤɤΡ֤ǡפäơ945 Ĥ#45166Ȼפޤ
P 945^10 * 1 * 3 * 5 * 7 * 9 * 11 * 13 * 15 * 17 * 19
1 * 3 * 5 * 7 * 9 * 11 * 13 * 15 * 17 * 19 25 * 3
äΤǡ
P 945^10 * 25 * 3
ϡ#45166Ρ
3x94510
Ȥäȹʤ
945^2 55^2 = 3025 25945^4 25^2 = 62525^2 * 25 = 625 * 25 125 * 5 = 625 = 25^2
ʤΤǡ
P 945^10 * 25 * 3 = 945^6 * 945^4 * 25 * 3
945^6 * 25^2 * 25 * 3 945^6 * 25^2 * 3
945^6 * 945^4 * 3 = 945^10 * 3
ȤʤäưפϤޤ͡¿ʬμѷ㤦ΤǤ礦
ˤ衤
P 945^10 * 25 * 3 945^10 * 3 25^5 * 3 = 625 * 25^3 * 3 625 * 3 = 1875 875
ĤޤꡤP β 875 Ǥ

ޤƱη׻ʤΤɤäƤƱǤ (^^;
910ڡ 13:39:30 45183
ޤ륱
ruby -e "p (1..50).to_a.map{|i|i*2-1}.inject(:*)%1000"
910ڡ 8:37:53 MAIL:take4310@mobile.email.ne.jp 45184
appoi-pangaea
ïФ
ѥ󥲥 910ڡ 11:30:56 45185
ޥ
#45182餫ߤ

ϤǤǤ䤵ޤ^^;
MacbookPro 910ڡ 12:38:22 45186
2N.K.
please
ˤ
????????????????????????????????????????????????????????? 910ڡ 18:07:51 45187

10ˤʤä ϲδۤȤȤ Ф뤫
910ڡ 21:46:14 45188
Ϸ
򻲹ͤ˼Τ褦ʲͭ
򼡤Τ褦˹ͤ
ص壵ʬϸǹθ
(10+1)(10-1)(10+7)(10-7)(10+3)(10-3)(10+9)(10-9)
ȾȸȾʬ
(10000-5000+49)(10000-9000+729)
Ĥ4ĤʬƹͤȲ3Ʊˤʤ
ߣ᣷
򣵾褹
ϣȤʤ
ʬ׻
ߣߡġߣ᣸

ߣ᣸

Ǹϲ夷ȤޤǤ
ʬˤƤƻ˷׻ޤ
ʤƤˡĤʤä
ʡ 910ڡ 21:52:20 45189
̤ꤹ1
ФƤʹơMỲ塪
Ǥϰ䡣
:ȬѷAޤ
դĹ4cmǡĺΤ4Ĥ4cmɳĤޤ
ΤȤ4ĤɳȬѷ̲Ǥΰϲcm^2Ǥ
ɳθߤϹͤ߼Ψ3.14Ȥޤ
񡡡 911 15:36:05 45192
Ȥ
Maxima

mod(99!!,1000);875
˭ԡ 911 16:16:17 MAIL:fttnm528@ybb.ne.jp 45193
٥륯åĥ
#45192
4ĤĺˤĤ4ܤɳΤɤ줫̲ǤϰϤκͤǤ礦
Ǥϡ4Ѥ45١135٤ʿԻշѤФʤޤ
911 21:16:50 45195
̤ꤹ1
#45195
ϰϤʤ顢դˡ̲ǤʤϰϤפˤʤޤ
ϤϤǤȤƲ
񡡡 912ʷ 18:48:24 45197

פ֤Ǥ
ɤäǸȤǤ
912ʷ 22:16:54 45198

#45186
ΤʤäΤǤοäƤޤ()
914ʿ 23:31:34 45199