Ȥ
basic

FOR a=1 TO 10000
IF MOD(a+2,5)=0 AND MOD(a+7,13)=0 AND MOD(a+41,31)=0 THEN PRINT a
NEXT a
END

f9ơ
1943()


˭ԡ 18ڡ 0:07:25 MAIL:fttnm528@ybb.ne.jp 42788
å
201551331ȡ2015ǯˤʤ䤤Ǥ^^
18ڡ 0:11:43 42789

#42789
ʤۤɡ
5*13*31-72ʤǤ͡
18ڡ 0:14:54 42790
4329ܤβ
2­5ܿˤʤꡢˤޤ5­13ܿˤʤ뤬13ܿ5ܿ5­ΤǤ뤿5ܿǤ⤢
ä7­65ܿˤʤ
Ȥ65-7=58Ϥޤꡢ65ɤɤ­Ƥ31dz21;Τõ1943Ĥ
18ڡ 0:15:37 42791
baLLjugglermoka
ᡣȤ

깹ʳԷǼĤϥ󤷤ƤʤäΤǡǯΰˤʤޤ
18ڡ 0:16:41 42792
ʪ
ޤ+4131ܿˤʤɽ롣
21,52,83,1912,1943,1974

+25ܿ+713ܿξ+5865ܿõ
̡1943
ܡ 18ڡ 0:16:48 42793
٥륯åĥ
ܥǹʤ˺Ƥޤ
ޤʤǤ褯˺Ƥޤ
18ڡ 0:26:19 42794
4329ܤβ
Хľ1Ĥ31dzä櫓ǤϤʤͤ
ޤ5831dz27;ꡢ6531dz3;Τǡ;οܤ27Ϥޤꡢ3Ƥ31Ķ31ͤˤʤΤǼΤ褦ˤʤ
27Ģ212427
ޤǤ65礦31­Ȥˤʤ
;꤬21ˤʤΤ2ʤΤ6529­Ф褤
ä(65-7)+6529=6530-7=1943
18ڡ 0:28:03 42795
!!!
μΤϤΤܤäۤ®礬¿Τ
1-2,-7,-12,,,
2-7,-20,-33,,,
3-41,-72,,,
5*13*31-72=1943
18ڡ 0:32:19 42796
٥륯åĥ
5dzä3;롢13dzä6;뢪65dzä58;롣
65dzä58;롢31dzä21;뢪1943
Ǿܿ2015ޤǤ˳μ¤ˤ뤳ȤʬäΤǡʾƬȤ鷺õޤ
18ڡ 0:37:40 42797
Mr.ǥ
41­ȡ31ܿˤʤ.....21,52,83,114,145,176,207,238,269,300,331,362,
Τ7­13dzǾΤ 331
41򤿤31dz졢7­13dzװ̹ϡ13*31*+331

󤹤ȡ331,734,1137,1540,1943,2346
Τ2­5dzǾΤΤϡ1943
Ȥޤ
18ڡ 0:51:56 42798
٥륯åĥ
ʤߤ1331դơ1ΰ̤38ˤʤΤĤͤдñǤ͡
18ڡ 0:49:52 42799
4329ܤβ
Хľ1Ĥ31dzä櫓ǤϤʤͤ
ޤ5831dz27;ꡢ6531dz3;Τǡ;οܤ27Ϥޤꡢ3Ƥ31Ķ31ͤˤʤΤǼΤ褦ˤʤ
27Ģ212427
ޤǤ65礦31­Ȥˤʤ
;꤬21ˤʤΤ2ʤΤ6529­Ф褤
ä(65-7)+6529=6530-7=1943
18ڡ 0:52:37 42800
⡼ޥ
#42790
ʤۤɤ
ߤʤ󥹥ޡȤ͢
ϢΩ򤤤Ƥޤޤ^^;

5*13*31-m
5a=m-2
13b=m-7
31c=m-41
m=72
ȤȯۤʤΤͤ(Orz)
֤...;Ʊͤ͡?
¨ ^^;v 18ڡ 1:31:19 42801

ޤƤǤȤޤ
ٶˤʤޤ
1ΰ̤ͤƥ򤭤ޤ
礭3958ʡ
18ڡ 2:48:24 HomePage:42802
ϥ饮㡼ƥ
ޤƤǤȤޤ
ǯĥޤΤǤꤤޤ

ǯνץߥ󥰤ˤʤޤ
18ڡ 6:42:20 HomePage:湩ؤ˥42803
zaki
1ꡢ7­Ƥ5ܿˤʤ롣
2碌ơ7­65ܿˤʤ롣
ơ72­Ƥ65ܿˤʤ뤳ȤˤǤ롣
372­31ܿˤʤ롣
Ǹ2Ĥ碌ȡ72­2015ܿˤʤ뤳Ȥ狼Τǡ
Ǿο
201572=1943

ǯꤤޤ
18ڡ 8:36:45 42804

Ϥ褦ޤ
-3, -8, -13, -18, ġ5ܿ
-6, -19, -32, -45, -58, ġ13ܿ
ʤΤǡ-5865ܿ
+7, +72, +137, +202, ġ65ܿ
+10, +41, +72, ġ31ܿ
ʤΤǡ+72=6531=2015ܿ
äƺǾΥ=2015-72=1943

褯Ĥޤ䤤dzμ¤˵ˤϤɤȤ褤Τʡ
ٶƤޤ
18ڡ 8:40:04 42805
ˤ
1ꡡ7ä5ܿˤʤ
2ȹ碌ȡ7ä65ܿˤʤ
äơ72ä65ܿˤʤ
3ꡡ72ä31ܿˤʤ
äơ72ä6531ܿˤʤ
18ڡ 8:44:36 42806

ޤƤǤȤޤ
ǯ⤳ˤ⤷ơޥ뤵(ǯˡáƲ)ߤʤβˡɤޤƤܤɻߤǤȻפäƤޤꤤޤ
18ڡ 8:51:45 42807
???
VBSCRIPT
deta=0:k=2
while deta=0
a=31*k-41
if ((a+2) mod 5)+((a+7) mod 13)=0 then
deta=1:msgbox a
else
k=k+1
end if
wend
18ڡ 10:12:28 42808
ϺĹ
ȯλ񤭹ߡ
ñ˸ơ񤷤äǤ
ǯǤȤޤ
18ڡ 10:45:12 42809
algebra
3mod 5ˡ
6mod 13ˡ
21mod 31ˡ

ꡤ58mod 65ˡ

ꡤ1943mod 2015

ޤˡ;פǤ͡
18ڡ 11:05:19 42810
ģ©
ǯߤȤϤפäΤǤˤʤäȤ
֣ǯסȾפäƤޤޤɤҤĤǯǤɡ

ޤƤǤȤޤǯꤤ夲ޤ
18ڡ 12:06:55 42811
uchinyan
Ϥˤϡơϡ
ϡŪˤͤξ;ʤɤȤΤƤͭ̾ʤΤǤ͡
ϤĤޤŪǤʤˡȤƤϡȯŪǤʴʡ

13 * 31 = 403 = 405 - 2 = 81 * 5 - 2
31 * 5 = 155 = 156 - 1 = 12 * 13 - 131 * 5 * 7 = 12 * 7 * 13 - 7
5 * 13 = 65 = 62 + 3 = 2 * 31 + 35 * 13 * 7 = 2 * 7 * 31 + 21 = 2 * 8 * 31 - 41
ʤΤǡǾθơ
= 13 * 31 * 1 + 31 * 5 * 7 + 5 * 13 * 7 = 403 + 1085 + 455 = 1943
ˤʤޤ

ʤߤˡ5 * 13 * 31 = 20152015 - 72 = 1943Ǥ͡
ͥνȡ 18ڡ 12:16:58 42812
masa
1,258+65m(m)ϻǤǤɤäɤ狼餺ŪˤʤäƤޤޤ
58+65m+41=99+65m=31(3+2m)+6+3m
6+3m=31n(n:)Ȥm=10n-2+1/3n nκǾͤ3 λm=29 ä=58+6529=1943
18ڡ 12:53:28 42813
masa
1,258+65m(m)ϻǤǤɤäɤ狼餺ŪˤʤäƤޤޤ
58+65m+41=99+65m=31(3+2m)+6+3m
6+3m=31n(n:)Ȥm=10n-2+1/3n nκǾͤ3 λm=29 ä=58+6529=1943
18ڡ 13:11:19 42814
uchinyan
ǼĤɤߤޤ
Ʊ褦ʲˡŪʲˡ줿ꤷޤޤơ

#42791#42795
2 ­ 5 ­ 13 ܿˤʤ뤳Ȥ餳줬 65 ܿˤʤ뤳Ȥ顤 = 65 ܿ - 7ȹͤơ
65 - 7 = 58 ȯˤơ31 dzä;ε§Ĵ١Ȥ˹ͤˡ

#42793#42798
;꤬Ʊɽäƹͤˡ

#42796
;򤵤Τܤäƹͤ 51331 κǾܿ 2015 72 Τˤʤ뤳Ȥ򸫤ĤƲ򤯲ˡ
#42804ʤɤȴŪˤƱǤ

#42797
5 dzä 3 ;ꡤ13dzä 6 ;뤳Ȥ顤65 dzä 58 ;ꡤ
65 dzä 58 ;ꡤ31dzä 21 ;롤Ȥˡ

#42799
1331դơ1ΰ̤38ˤʤΤĤͤ
Ȥˡܺ٤Ǥ
¿ʬ#42797ǡ13 dzä 6 ;ꡤ31dzä 21 ;롤˹ͤΤǤ礦

#42801#42813#42818
򼰤ˤƤˡ

#42802
ΰ̤οܤƻĴ٤ˡ

#42804#42805#42806
5 dzä 13 dzä狼顤 7 ­ 65 ܿǡ 72 ­Ƥ 65 ܿ
ǡ31 dzä⡤ 72 ­ 31 ܿäơ 72 ­ 2015 ܿ
ȤȤˡ
ĿŪˤϡȤƤϤ餬ʤȻפޤ

#42810#42819
Ʊˤˡ
ʤ#42819ϸܤϤʤ㤤ޤ桼åɤθ߽ˡطʤˤȤ̣Ǥϡ
#42812ιƱǡǤȸäƤ⤤Ǥ礦

#42812
13 * 31 = 403 = 405 - 2 = 81 * 5 - 2
31 * 5 = 155 = 156 - 1 = 12 * 13 - 131 * 5 * 7 = 12 * 7 * 13 - 7
5 * 13 = 65 = 62 + 3 = 2 * 31 + 35 * 13 * 7 = 2 * 7 * 31 + 21 = 2 * 8 * 31 - 41
ܤƲ򤯲ˡβˡطʤϼ¤ϥ桼åɤθ߽ˡǤ

#42788#42803#42808
ץˤˡ
ͥνȡ 19ʶ 13:38:35 42815
̵
졢ˤ㤦ȡ-1943פȤ⤢ʤΤǡ
̵¤˾ϤȤ㤦󤸤ʤǤ
18ڡ 17:55:33 42816

#42816
οذǯǽΤ
Ūˤ0,1,2,
ȤȤǤΤǤϤʤǤ礦(^^;
18ڡ 18:45:12 42817
ǯ
A򸵤οȤơA+2=5X, A+7=13Y, A+41=31Z
13Y-5X=5 13Y=5(X+1)513ϸߤǤʤΤY=5NNˤȽ񤱤롣
ޤ31Z-13Y=31Z-65N=A+41-A-7=34
ϤޤѷС31Z-65N=31(Z+1)-65(N+1)-31+65=31(Z+1)-65(N+1)+34=34
Τˡ31(Z+1)=65(N+1)Ǥꡢ3165ߤǤʤΤǡZ+165ܿ
Z=64ȤơA=31*64-41=1943
18ڡ 19:40:58 42818
(Keigei)
īϻ֤ʤäΤǡ񤭹ޤǤ

1331 κǾܿ 4033 (mod 5) 40328061 (mod 5)
315 κǾܿ 15512 (mod 13) 1551218601 (mod 13)
513 κǾܿ 653 (mod 31) 652113651 (mod 31)
ޤ51331 κǾܿ 2015 Ǥ
äơ806a1860b1365c 5dzä; a13dzä; b31dzä; c Ǥ
N 5dzä;꤬ a13dzä;꤬ b31dzä;꤬ c ǤС
N806a1860b1365c (mod 2015) Ǥ
Ǥϡa3b6c21 顢
N806318606136521422431943 (mod 2015) ˤʤޤ
18ڡ 19:52:46 42819
ޤ
#42789 å㤵
> 201551331ȡ2015ǯˤʤ䤤Ǥ^^

ϥ ߥ̥롡Υˡ勵ϡʥ꥿
somewhere in the world 18ڡ 22:41:13 42820
CRYING DOLPHIN
ޤƤǤȤޤ
ǯꤤޤ롪

ǯGW쥪դλäͽŪ񤷤orz
ï⤤ʤԳϡ 18ڡ 22:43:06 HomePage:֥⤢42821
ϥ饮㡼ƥ
ȤʤȻפä
ɽǯȻƤޤ

⤦ǧˡΥƥȤǤʤϡ
Ȥ
ϲȤʹФˤʤޤ
19ʶ 6:54:52 HomePage:湩ؤ˥42822

IJ򸫤ĤƤȤn=5*13*31+ηˤޤ

. n=5*K+3
. n=13*L+6
. n=31*M+21

ƱȤ롣ξդˣ­ơ줾
. n+7=5*K+10=5*(K+2)
. n+7=13*L+13=13*(L+1)

5*(K+2)=13*(L+1)ꡢK=11,L=4,n=58
lcm(5,13)=65μnĤ뤳Ȥ餫ʤΤ
. n=65*A+58(a0ʾˤɽ롣

˲ä˥ϤϡʲޤȤ˷׻
n=65*A+58
n=31*M+21

65*A+58=31*M+21
M=2*A+1+3*(A+2)/31
3*(A+2)/31ǤȤA=29ΤҤȤĤǤ롣
äơn=65*29+58=1943Ϥΰġ
lcm(65,31)=65*31Ǥ롣
ǰΤ n-65*31=-2*65+580Ǥ뤳Ȥǧ
n=1943βȤƤϺǾ
̲n=5*13*31*k+(58-2*65)=2015*k-72
110ڡ 16:21:48 42823
maple
ޤ2ܤ3ܤǹͤȡ331˸Ĥ롣ˤʹߤ1331403­Ƥäˤʤ롣
ǡ1ܤϰΰ̤38Ǥ뤫顢­ƤȺǽ1943Ĥ롣
⤷γǰȤСưפ-72Ĥꡢ2015­1943ˤʤޤ

(ͤǤꤤޤ)
111 20:41:21 42824