Taro
äȻͼθǹͤƤޤ()
914ڡ 0:05:24 28227
ޥ
դߥʤä褦ư¿...˿ڡι򤷤ƤޤơȤ˥ߥΩʤΤ..
PowerBook G4 914ڡ 0:06:40 MAIL:masaru-y@sansu.org HomePage:28228
sugitakukun
16x-1Ǥ뤳ȤޤǤ϶餯1ʬäǤ礦
ʤǡ֣פorz
⣲|li orz il|
914ڡ 0:16:06 28229

פ֤ˤλ֤˼ˤޤ顢źʪĤ볤ΡʤȤäƤ᤯ʤǤ˹츫ؤΥĥ˹ԤäƤޤ
914ڡ 0:24:10 28230
ޥ
ơ𤷤ޤ𤷤ߥĤäƤ...ʤƤȤˤʤäƤʤɤΤǤ..
PowerBook G4 914ڡ 0:27:48 MAIL:masaru-y@sansu.org HomePage:28231

ŪΤǤʤ롢ͤ᤮ʡ
914ڡ 0:28:47 28232
sugitakukunνĩ
ĩǤ
ʸ򤭤ɤǤʤơȤܤ٤äƤޤޤOTL
914ڡ 0:29:06 28233
Ȥ
ʲΤ褦˽basictruncateڤΤ
䤹褦10ifǹʤޤ

FOR a=1 TO 100
FOR b=1 TO 100
LET x=16*a/7
LET y=16*b/9
LET z=TRUNCATE(x,0)
LET w=TRUNCATE(y,0)
IF z<=20 and w<=20 and 10<z and 10<w THEN PRINT z;w
NEXT b
NEXT a
END

9֤Ǥä
15,31,47,63,79,956ġ
˭ԡ 914ڡ 0:31:14 MAIL:fttnm528@ybb.ne.jp 28234
Masa
ǡߤ16ܿˤĤƤϡڼΤƤʤƤOKʤǤ͡ȤϡAξ(16dzäơ;ڤΤƤȤ˽ФƤ)24691113ˤʤꡢBξ(16dzäơ;ڤΤƤȤ˽ФƤ)13578101214ˤʤ롢ȤȤ˵ŤС16dzä15;ФƤʤ櫓Ǥ͡
914ڡ 2:17:21 28235
Ф
񤭽Ф줷פ⤫Фʤ
914ڡ 2:31:16 28236
ϥ饮㡼ƥ
Ϥ褦ޤץǤ
MATLABǤ
914ڡ 8:46:07 HomePage:湩ؤĩ28237
⡼ޥ
10<16/7*x<100xθĿ=43-4=39
10<16/9*y<100yθĿ=56-5=51
̤Τϡ16ܿʤΤǡ99/16=6
οϡ99-9=90 ġ
Ĥޤꡢ
90-(39+51-6)=6
39+51=90 Ϥޤޡ
914ڡ 9:06:42 28238
uchinyan
Ϥˤϡϡäơ٤ޤ
꼫Τϡ§Ĵ٤ФʤΤǡŪñʡȻפޤ
ޤ16/7 ˴ؤƤϡ
0 * 16/7 = 0 + 0 -> 0
1 * 16/7 = 2 + 2/7 -> 2, 2
2 * 16/7 = 4 + 4/7 -> 4, 2
3 * 16/7 = 6 + 6/7 -> 6, 2
4 * 16/7 = 8 + 8/7 -> 9, 3
5 * 16/7 = 10 + 10/7 -> 11, 2
6 * 16/7 = 12 + 12/7 -> 13, 2
7 * 16/7 = 14 + 14/7 -> 16, 3
8 * 16/7 = 16 + 2 + 2/7 -> 18, 2
9 * 16/7 = 18 + 2 + 4/7 -> 20, 2
...
ʤΤǡ٤礦ϡ
2, 2, 2, 3, 2, 2, 3, ... 7 ǰʲ֤...
ˤʤޤϡפˡ2/7 ܤʬǤ͡νиλ顢餫Ǥ
Ʊͤˤơ16/9 ϡ
0 * 16/9 = 0 + 0 -> 0
1 * 16/9 = 1 + 7/9 -> 1, 1
2 * 16/9 = 2 + 14/9 -> 3, 2
3 * 16/9 = 3 + 21/9 -> 5, 2
4 * 16/9 = 4 + 28/9 -> 7, 2
5 * 16/9 = 5 + 35/9 -> 8, 1
6 * 16/9 = 6 + 42/9 -> 10, 2
7 * 16/9 = 7 + 49/9 -> 12, 2
8 * 16/9 = 8 + 56/9 -> 14, 2
9 * 16/9 = 9 + 63/9 -> 16, 2
10 * 16/9 = 10 + 7 + 7/9 -> 17, 1
11 * 16/9 = 11 + 7 + 14/9 -> 19, 2
...
ʤΤǡ٤礦ϡ
1, 2, 2, 2, 1, 2, 2, 2, 2, ... 9 ǰʲ֤...
ˤʤޤ⡢פˡ7/9 ܤʬǤ͡νиλ顢餫Ǥ
äơĤϡ
16/7 ϡ2, 4, 6, 9, 11, 13, 16, ...
16/9 ϡ1, 3, 5, 7, 8, 10, 12, 14, 16, ...
ȤʤꡢĤ碌ȡ 16 Ĥ󤬰פΰȴ롢ȤȤˤʤޤ
äơȴΤϡǤϡ15, 31, 47, 63, 79, 95 6 Ĥˤʤޤ

Ū˽񤭤ޤμä7, 9 ϸߤǡ16 = 7 + 9򸵤ˡ
ޤޤȤСޡȤʲˡˤʤΤʡȤޤ
ޤ̣餫Ǥɤʤ񤫤ƤǽʬǤ礦 (^^;
ͥνȡ 914ڡ 12:06:34 MAIL:uchi@sco.bekkoame.ne.jp 28240
uchinyan
Ǽɤߤޤ

#28227
ࡢͼθ#28240ǹͤƤߤȡ

ޤ16/7 ˴ؤƤϡ
0 * 16/7 = 0 + 0 0 -> 0
1 * 16/7 = 2 + 2/7 -> 2, 2
2 * 16/7 = 4 + 4/7 -> 5, 3
3 * 16/7 = 6 + 6/7 -> 7, 2
4 * 16/7 = 8 + 8/7 -> 9, 2
5 * 16/7 = 10 + 10/7 -> 11, 2
6 * 16/7 = 12 + 12/7 -> 14, 3
7 * 16/7 = 14 + 14/7 -> 16, 2
8 * 16/7 = 16 + 2 + 2/7 -> 18, 2
9 * 16/7 = 18 + 2 + 4/7 -> 21, 3
...
ʤΤǡ٤礦ϡ
2, 3, 2, 2, 2, 3, 2, ... 7 ǰʲ֤...
ˤʤޤƱͤˤơ16/9 ϡ
0 * 16/9 = 0 + 0 0 -> 0
1 * 16/9 = 1 + 7/9 -> 2, 2
2 * 16/9 = 2 + 14/9 -> 4, 2
3 * 16/9 = 3 + 21/9 -> 5, 1
4 * 16/9 = 4 + 28/9 -> 7, 2
5 * 16/9 = 5 + 35/9 -> 9, 2
6 * 16/9 = 6 + 42/9 -> 11, 2
7 * 16/9 = 7 + 49/9 -> 12, 1
8 * 16/9 = 8 + 56/9 -> 14, 2
9 * 16/9 = 9 + 63/9 -> 16, 2
10 * 16/9 = 10 + 7 + 7/9 -> 18, 2
11 * 16/9 = 11 + 7 + 14/9 -> 20, 2
...
ʤΤǡ٤礦ϡ
2, 2, 1, 2, 2, 2, 1, 2, 2, ... 9 ǰʲ֤...
ˤʤޤäơĤϡ
16/7 ϡ2, 5, 7, 9, 11, 14, 16, ...
16/9 ϡ2, 4, 5, 7, 9, 11, 12, 14, 16, ...
Ȥʤꡢ 16 κǽμޤǤȴΤ 7 Ĥˤʤޤ
äơ100 ޤǤȴΤϡ100 = 6 * 16 + 4 ǡ97, 99 ȴΤ˺줺 6 * 7 + 2 = 44 ġ
Ǥϡ44 - 4 = 40 Ĥˤʤޤ
ʤ㤤ޤ͡

ʤߤˡڤ夲Ǥϡ
16/7٤礦ϡ3, 2, 2, 3, 2, 2, 2, ... 7 ǰʲ֤...
16/9٤礦ϡ2, 2, 2, 2, 1, 2, 2, 2, 1, ... 9 ǰʲ֤...
ˤʤޤäơĤϡ
16/7 ϡ3, 5, 7, 10, 12, 14, 16, ...
16/9 ϡ2, 4, 6, 8, 9, 11, 13, 15, 16, ...
Ȥʤꡢ 16 κǽμޤǤȴΤ 1 1 Ĥˤʤޤ
äơ100 ޤǤȴΤϡ100 = 6 * 16 + 4 ǡ97 ȴΤ˺줺 6 * 1 + 1 = 7 ġ
Ǥϡ7 - 1 = 6 ĤˤʤꡢڤΤƤξƱǤޤǤ͡

#28229, #28235
ܤϡ#28240ƱǤ͡
餯Dz򤫤Ƥ¿ΤȻפޤ

#28234
äѤäɤǤ͡ʤߤ˻ä顢뤫ʡ

REM ˥󥸣
REM OPTION ARITHMETIC RATIONAL
DIM p(100)
LET c = 0
FOR i = 1 TO 100
LET a = INT(16*i/7)
LET b = INT(16*i/9)
REM LET a = ROUND(16*i/7)
REM LET b = ROUND(16*i/9)
IF a < 100 THEN
LET p(a) = p(a) + 1
END IF
IF b < 100 THEN
LET p(b) = p(b) + 1
END IF
NEXT i
FOR i = 10 TO 99
IF p(i) = 0 THEN
LET c = c + 1
END IF
REM PRINT i; p(i)
NEXT i
PRINT c
END

ʤLET a = INT(16*i/7) ΤȤLET a = INT(16/7 * i) Ȥȡ
ͭ⡼ɤǷ׻ʤȤޤʤ礬褦Ǥ
ʥ١åνϤη׻θ³Ǥ褦Ǥʬ뤫ʡ

#28236
ʤС񤭽ФǤ礷ȤϤʤǤ礦
ƻǤμ¤ˡ⤷ʤ

#28237
MATLABϡˤʬʤΤǡ(^^;

#28238
ʤۤɡ
x Ȥơ16/7 * x ʬͤ x ۤʤФ٤ưۤʤΤǡʬͤ x Ȥϣ16/9 * y Ʊ͡
äơ16/7 * x ʬͤθĿ x θĿƱy Ʊ͡
Ĥޤꡢx, y ǿĿϡбˤäơʬθĿʤꡢ
ڤΤƤ顢10 100 ϰϤǡ16/7 * x ʬͤθĿ 39 ġ16/9 * y ʬͤθĿ 51 ġ
ޤڤΤƤ顢ʬǡ
䶦̤Τϡ16ܿʤΤǡ99/16=6
ɡ
90-(39+51-6)=6
ǤΤϡ򤤤ʤ
ʤͼθξˤϡֶ̤Ρפʣˤʤꡢ 16 γƼȤ 7 ĤǡǸ 98 ˤʤޤ
ǡơ̤Τ 7 * 6 + 1 - 4 = 39 Ǥ
ޤ16/7 * 4 = 9.14, 16/7 * 43 = 98.28, 16/9 * 5 = 8.88, 16/9 * 56 = 99.55 ʤɤդȡ
16/7 * x ʬͤθĿ 39 ĤǤ16/9 * y ʬͤθĿ 50 Ĥˤʤޤ
Ĥޤꡢͼθξϡ10 100 ϰ¤ǣб̯ʥ줬Фޤ
ޤǤСƱͤˤơ90 - (39 + 50 - 39) = 40 ġˤʤޤ͡
39+51=90 Ϥޤޡ
󡢤ɤʤǤ礦
ͥνȡ 914ڡ 15:05:54 MAIL:uchi@sco.bekkoame.ne.jp 28241

Τۤϣ
ΤۤϣΤ
Ƿ׻ƤȣΣĤˤʤ롣
ޤǽΣʬФ飱ƤдñˤʤΤǤɡϤϤϤϤϡ򤯤Τˣʬ⤫äʬ
𤱤ʤǤ
914ڡ 18:22:42 28242
N.Nishi
ơ󤷤ޤ
914ڡ 20:43:06 28243
⡼ޥ
#28240
uchinyan
>7, 9 ϸߤǡ16 = 7 + 9
餹ȡ
39+51=90 Ϥޤޡ
ϡ
16=3+13=5+11 Ǥʤꤿ
ºݤˡ[300/16]-[30/16]=18-1=17,[1300/16]-[130/16]=81-8=73 ǡ
17+73=90
褯ߤȡ[100*3/16]+[100*13/16]-([10*3/16]+[10*13/16])
=[100(3+13)/16]-[10(3+13)/16] ʤ顢˸ޤ͡
äƸΤǤ礦
914ڡ 22:16:30 28244
ʸ
˺Ƥ
16n-1äݤΤ
6Ĥʡ

914ڡ 23:36:07 MAIL:kyorofumi@msn.com HomePage:ʸ28245
ߤγ
ABʬˤм狼䤹Ȼפޤ
μȤˤ줾񤭽Фȡ28235MasaƱ
16dzä;꤬15ˤʤǤʤȵդޤ

ʼ˸ 915ʶ 0:36:46 28246
ˤ
28246
ABʬˤм狼䤹פƱ
A뤳ȤǤʤΤϡ16ǽब10121415,17,19,21,23,24ΤΡ
B뤳ȤǤʤΤϡ16ǽब1113,15,18,20,22,25ΤΡ
̤Τϡ16ǽब15ΤΡ
ϻʤ⤷ʤɡ
915ʶ 6:08:20 28247
ڼ
ʬҤǡʬ줬ʣݣˤȡʣܣˤξˤϡ
ǣĤФƤʤΤǤϡ
Ǥ
͡ 915ʶ 6:40:58 MAIL:iida@ae.keio.ac.jp 28248
uchinyan
#28244
>7, 9 ϸߤǡ16 = 7 + 9
񤭹ߤʤä褦ʤΤǡޤĥä򤷤Ƥޤ礦

a, b, a > b > 0 ϸߤǤȤơ(a+b)/a, (a+b)/b ˤĤơ#28240˴ŤƹͤƤߤޤ
m, n Ȥơ
m(a+b)/a = m + mb/a, n(a+b)/b = n + na/b
ʤΤǡʬϡm, n ä˽äơ줾 1 ʾäޤ
ǡm(a+b)/a ƱΤϤʤn(a+b)/b ˤƱΤϤޤ
ˡmb, na 򤽤줾 a, b dzäƾ p, q ; s, t, 0 <= s < a, 0 <= t < b ǽ񤯤
m(a+b)/a = (m+p) + s/a, n(a+b)/b = (n+q) + t/b
Ƚ񤱤ΤǡʬʤΤ m+p = n+q Ȥʤꡢ
m(a+b)/a - s/a = n(a+b)/b - t/b
mb(a+b) - sb = na(a+b) - ta
ta - sb = (na - mb)(a + b)
(t + s)a - s(a + b) = (na - mb)(a + b)
a, b ϸߤǤʤΤǡt + s a + b ˤɬפޤs, t μϰϤ餷ơs = t = 0 Ǥ
ǡ
mb(a+b) = na(a+b)
mb = na
Ƥӡa, b ߤǤʤΤǡm a ܿn b ܿˤʤޤ
Ĥޤꡢ(a+b)/a ʬϼ a(a+b)/b ʬϼ b ǡפޤ
(a+b)/a ʬ(a+b)/b ʬϡ줾Ǥϰפ뤳ȤϤʤäΤǡ
(a+b)/a ʬϣ a ġ(a+b)/b ʬϣ b ġ碌 a+b Ĥޤ
Ȥ(a+b)/a ʬ a ܤȤˤ(a+b)/b ʬ b ܤȤˤ a+b ǰפΤǤ顢
Թ硢1 a+b ǡa+b-1 Ĥΰۤʤ뤳Ȥˤʤޤ
ơǤϡ1 a+b ǡɤȴ뤫Ǥ¤ϡa+b-1 Ǥ
ϡ⤷1 a+b ǡĤޤꡢ1 <= m <= a
m(a+b)/a = (a+b-1) + s/a
Ƚ񤱤Ȥȡ
m(a+b) = a(a+b-1) + s
0 <= (a-m)(a+b) = a - s <= a
m = a ꤨޤ󤬡 a - s > 0 ʤΤǡ̷⤷ޤ
ȴΤϰĤʤΤǡɡȴΤ a+b-1 ˤʤޤ
ǡ̤ˡȴΤϡn Ȥơ(a+b)n - 1 ˤʤޤ
äơξθĿϡ̯Ǥäȡ[ ] ̾ΥεȤơ
[100/(a+b)] - [10/(a+b)] ˤʤ褦Ǥ

ơ
39+51=90 Ϥޤޡ

褯ߤȡ[100*3/16]+[100*13/16]-([10*3/16]+[10*13/16])
=[100(3+13)/16]-[10(3+13)/16] ʤ顢˸ޤ͡
䤳äƸΤǤ礦
餹ȡ̤ˤϡ̯Ǥ͡

̤ˡޤǤ a/(a+b) = 0.d1d2d3d4, d1, d2, ... Ͼʬγư̤οȤȡ
b/(a+b) = 1 - a/(a+b) = 1 - 0.d1d2d3d4 = 0.(9-d1)(9-d2)(9-d3)(9-d4)
Ǥͭ¾ξϡʬκǸ夬 10-di Ѥդޤ
ǡ
1) a/(a+b) = 0.d1d2, b/(a+b) = 0.(9-d1)(9-d2) ξ
[100 * a/(a+b)] = [d1d2.] = d1d2
[100 * b/(a+b)] = [(9-d1)(9-d2).] = (9-d1)(9-d2)
[10 * a/(a+b)] = [d1.d2] = d1
[10 * b/(a+b)] = [(9-d1).(9-d2)] = (9-d1)
[100 * a/(a+b)] + [100 * b/(a+b)] - [10 * a/(a+b)] - [10 * b/(a+b)]
= d1d2 + (9-d1)(9-d2) - d1 - (9-d1)
̾νǤϡ
= 10 * d1 + d2 + 10 * (9 - d1) + (9 - d2) - d1 - (9 - d1)
= 99 - 9
= 90
ǡ
[100 * (a/(a+b) + b/(a+b))] - [10 * (a/(a+b) + b/(a+b))]
= 100 - 10
= 90
ʤΤǡפޤ
2) a/(a+b) = 0.d1, b/(a+b) = 0.(10-d1) ξ
[100 * a/(a+b)] = [(d1)0] = (d1)0
[100 * b/(a+b)] = [(10-d1)0] = (10-d1)0
[10 * a/(a+b)] = [d1] = d1
[10 * b/(a+b)] = [(10-d1)] = (10-d1)
[100 * a/(a+b)] + [100 * b/(a+b)] - [10 * a/(a+b)] - [10 * b/(a+b)]
= (d1)0 + (10-d1)0 - d1 - (10-d1)
̾νǤϡ
= 10 * d1 + 0 + 10 * (10 - d1) + 0 - d1 - (10 - d1)
= 100 - 10
= 90
ǡϤꡢפޤ
3) a/(a+b) = 0.d1d2, b/(a+b) = 0.(9-d1)(10-d2) ξ
[100 * a/(a+b)] = [d1d2] = d1d2
[100 * b/(a+b)] = [(9-d1)(10-d2)] = (9-d1)(10-d2)
[10 * a/(a+b)] = [d1.d2] = d1
[10 * b/(a+b)] = [(9-d1).(10-d2)] = (9-d1)
[100 * a/(a+b)] + [100 * b/(a+b)] - [10 * a/(a+b)] - [10 * b/(a+b)]
= d1d2 + (9-d1)(10-d2) - d1 - (9-d1)
̾νǤϡ
= 10 * d1 + d2 + 10 * (9 - d1) + (10 - d2) - d1 - (9 - d1)
= 100 - 9
= 91
ǡפޤ
äơȤ̣Ǥϡ̤ˤϡΩޤ

ξϡ׻ʬ褦ˡ100 ܤΤˤʤäƤޤ
ȤȤΩ֤ȡο˸ꤷƹͤΤǡ
10 < (a+b)/a * x < 100, 10 < (a+b)/b * y < 100
Ȥʤ x, y θĿ櫓Ǥ3) ξ 100 礦ܿˤʤäƤΤǡ
[100 * a/(a+b)] + [100 * b/(a+b)] ȤȤ꤬褦Ǥ
Ūˤϡ100 ơ[100 * a/(a+b)] + [100 * b/(a+b)] - 2 ȤʤФʤޤ
ȡ٤ 91 - 2 = 89 = 90 - 1 ˤʤޤǤΤǤ

ȤȤϡ餫顢 [100/(a+b)] - [10/(a+b)] Το 90 Ȥˤʤޤ
1), 2) ξϡ[100/(a+b)] - [10/(a+b)] ˤʤޤ
3) ξϡa, b ߤǤǤ뤳Ȥ顢a+b 100 ǤʤȤʤʤޤ
Ǻ٤ϡ[100/(a+b)] ꤬ϡ[100/(a+b)] - 1 - [10/(a+b)] ȤʤФʤޤ
Τǡ̤ϤϤ [100/(a+b)] - [10/(a+b)] ˤʤ褦Ǥ
ϡǽ˵᤿̤ȰפƤޤ
ɡ
39+51=90 Ϥޤޡ
ϡɬΤ褦ǤҤ٤褦ɬפʾ⤢ޤ

#28248
ʬҤǡʬ줬ʣݣˤȡʣܣˤξˤϡ
䣱ǣĤФƤʤΤǤϡ
餫Ǥ2n-1 = ga, 2n+1 = gb, a, b ϸߤǡȤȡg(b-a) = 2, g = 2 ϤʤΤǡg = 1 ǡ
2n-1, 2n+1 ϸߤǡäơޤǤεƧޤȡǤ͡
ͥνȡ 915ʶ 14:24:04 MAIL:uchi@sco.bekkoame.ne.jp 28250
⡼ޥ
#28250
>ǡ̤ˡȴΤϡn Ȥơ(a+b)n - 1 ˤʤޤ äơξθĿϡ̯Ǥ
[ ] ̾ΥεȤơ
[100/(a+b)] - [10/(a+b)] ˤʤ褦Ǥ

ʤۤɡ
Τˤϡ
a,b ߤǤʻεĿϡ
9<(a+b)n-1<100 顢
10<(a+b)n<101 ʤΤǡ
10/(a+b)<n<101/(a+b) Ȥʤꡢ
n θĿ=[101/(a+b)]-[10/(a+b)]ʡ
915ʶ 17:01:37 28251
⡼ޥ
#26251
ְ㤤ǤOrZѥɤäƤƽľʤä
10<=(a+b)n-1<=99 顢
11/(a+b)<=n<=100/(a+b) ȤʤΤǡäѤɡ
[100/(a+b)]-[10/(a+b)] ˤʤޤ͡
915ʶ 17:28:57 MAIL:crazy_tombo@yahoo.co.jp 28252
̵Τ15
16/7Ǥ16/9Ǥʤ16ʲο15顢
1516n(n0,1,2,3)Ǥ蘆Ϻʤ
ο100ʲʤΤn0,,5η6
ʤ󤳤Τ褦˥ѥŪΤºɤޤ
ͤХȤǿؤäƤޤʤʤפ褦ˤʤơorz
916ڡ 4:51:48 28256
⡼ޥ
ͧ䤬ޤ
錄ϥԥȤޤǤ


xyx^2+yy^2+xʿ
ˤʤ뤳ȤϤ뤫

916ڡ 13:51:49 28257
ޥ
#28258
ϡͥͭθХѥǤ󡢻ȤΩĤ褦˲ϤƤޤ....Ȥ櫓ǡºɤˤͤޤΤ..(^^;
PowerBook G4 916ڡ 16:44:48 MAIL:masaru-y@sansu.org HomePage:28258
weapon
#28257
x<=yΤȤy^2<y^2+x<y^2+2y+1=(y+1)^2
y<xΤȤx^2<x^2+y<x^2+2x+1=(x+1)^2
äơx^2+yy^2+xȤ˴ʿˤʤ뤳ȤϤʤ
916ڡ 17:12:09 28259
⡼ޥ
#28259
weapon򡪡
x^2 (x+1)^2 δ֤οˤʤäƤФǤ͡(^^)
917 0:06:09 MAIL:crazy_tombo@yahoo.co.jp 28260
uchinyan
(㴳ɲýޤ)
#28257, #28259, #28260

xyx^2+yy^2+xʿ
ˤʤ뤳ȤϤ뤫
˽٤Ƥޤޤ (^^;
ɤƱȤȻפޤweaponβˡˤϵڤӤޤ󤬡䤬򸫤ƻפäˡ

x^2 < x^2 + y ʤΤǡ⤷x^2 + y ʿˤʤʤСm Ȥơ
x^2 + y = (x + m)^2
Ƚ񤱤ϤǤƱͤˤơ⤷y^2 + x ʿˤʤʤСn Ȥơ
y^2 + x = (y + n)^2
ǡξȤⴰʿˤʤȤ顢
x^2 + y = (x + m)^2
y^2 + x = (y + n)^2
Ȥʤ褦ʼ x, y, m, n ¸ߤϤǤѷơ
2m * x - y = - m^2
x - 2n * y = n^2
餫顢
(1 - 4mn) * x = n^2 + 2 * m^2 * n
(1 - 4mn) * y = m^2 + 2 * m * n^2
ξαաxy ʤΤǡ1 - 4mn > 0 Ǥ褦ʼ m, n ¸ߤޤ
äơξȤⴰʿˤʤ뤳ȤϤʤȤˤʤޤ

ʤäȳĥꡢa, b ⼫Ȥơ
x^2 + ay, y^2 + bx ξȤⴰʿˤʤ뤳ȤϤ뤫
⡢ϡƱͤ˹ͤޤ
x^2 + ay = (x + m)^2
y^2 + bx = (y + n)^2

2m * x - a * y = - m^2
b * x - 2n * y = n^2
(ab - 4mn) * x = a * n^2 + 2 * m^2 * n
(ab - 4mn) * y = b * m^2 + 2 * m * n^2
ǡۤɤƱͤ ab - 4mn > 0 Ǥab - 4mn ʤΤǡab - 4mn >= 1 ȤǤޤ
ǡab >= 4mn + 1 >= 5 ɬפǤΤȤդ ab - 4mn ˤƤСx, y Ϸޤޤ
㤨Сab - 4mn = 1Ĥޤꡢab 4 ʾǤäơ4 dzä 1 ;ΤȤ
m, n mn = (ab - 1)/4 Ȥʤ褦ˤȤС
x = a * n^2 + 2 * m^2 * n
y = b * m^2 + 2 * m * n^2
Ȥ򤬤뤳Ȥʬޤ
ǰʤ顢Ū˾ĤΤѤǡ褯ʬäƤޤ (^^;

(ʲɲ)
ʥ֤ǤäѤäפĤޤ
x, y, m, n Ȥơx^2 + y = m^2, y^2 + x = n^2 ˤʤäȤޤȡ
y = m^2 - x^2 = (m + x)(m - x)
ǡp, q Ȥơ
y = pq, m + x = p, m - x = q, x = 1/2 * (p - q) ----- (1)
Ƚ񤱤ޤǡx >= 1 ꡢp >= q + 2 >= 3, y >= 3 ˤʤޤ
Ʊͤˤơr, s Ȥơy^2 + x = n^2 顢
x = rs, n + y = r, n - y = s, y = 1/2 * (r - s) ----- (2)
y >= 3 äΤǡr >= s + 6 >= 7, x >= 7 ˤʤޤ
ȡ
x >= 7 (1) ˺ŬѤơp >= q + 14 >= 15, y >= 15
y >= 15 (2) ˺ŬѤơr >= s + 30 >= 31, x >= 31
x >= 31 (1) ˺ŬѤơp >= q + 62 >= 15, y >= 63
y >= 63 (2) ˺ŬѤơr >= s + 126 >= 31, x >= 127

ȡɤޤǤ³뤳ȤǤޤ
ϡx, y β¤̵ˡäơx, y ̵ˤʤ뤳Ȥ̣x, y ¸ߤȤȤ̷⤷ޤ
äơx^2 + y = m^2, y^2 + x = n^2 ˤʤ뤳ȤϤʤȤˤʤޤ

ʤߤˡx^2 + ay, y^2 + bx γĥξˤϡa, b 򤦤ޤȤ x, y Τ礭ǤΤǡ
Τ褦ˤȤä a, b ФƤϡΤ褦̷ȯޤ

weaponβˡǡ y <= x ΤȤϡx^2 < x^2 + y < (x+1)^2 Ǥ
ϡ x^2 + y ʿͭˤ⡢ʤ餺̵ˤʤ롢ȤüŪ˼Ƥޤ
嵭Τ褦ʾ򸫤ȡ̵̵¤ΤƤ褦ʵ⤷ơʤʤ⤷ޤ͡
ͥνȡ 918ʷ 14:21:00 MAIL:uchi@sco.bekkoame.ne.jp 28262
粬ҹ
פ֤ޤʡˡϣʤΤǣʿ夲Ƥ⤽ϫϤʤʡ
νФƤʤ

ɤȣŤƤΤǰ°פͽ¬ưŻޤʡ
פ֤β̵ϤϤɤǤ͡äƤϡͤʤ褦ˤ褦
917 15:51:56 MAIL:toshi009@land.hokuriku.ne.jp 28263
⡼ޥ
#28262
uchinyan󡢤ͻ꤬ȤޤOrZ

դȻפäΤǤʤøǤߤޤ󡦡

a^2+b^2=c^2 ˤƤϤȡa=x,b^2=y ʤ顢c 롣
ΤȤy^2+x=z^2 ˤʤ뤿ˤϡx=m^2 ʤ¸ߤ롣
Ĥޤꡢx=m^2,y=b^2 ΤȤ
x^2+y=(m^2)^2+b^2=c^2
y^2+x=(b^2)^2+m^2=n^2
ƱΤʤȤǤϤɤʤ

Ǥ̷⤬ʤȤʤϤǤ͡
ֻʤƤ빽ǤΤǡ(^^)
917 21:09:27 28264
uchinyan
#28264
ƤˤϡĤۤɡˤʤޤ

ܤϡΤˡx = a, y = b^2 Ȥơx^2 + y = a^2 + b^2 = c^2 Ȥʤ x, y, c Ǥޤy ʿǤʤȤ⹽ʤǤ
㤨С2^2 + 5 = 4 + 5 = 9 = 3^2 ʤɡ
ƤˡǤϡǽӽʤ褦ʵޤ

ܤϡ夬äƤޤΤǡ̤ˤ񤷤ʤꤽʵǤ褬ƤФΤǤ
#28262Ǥϡषx, y ˴ؤƤϰ켡ʤ褦˹פޤ
Τǡϸ̤褯ʤä褦˴Ƥޤ
ͥνȡ 917 22:31:41 MAIL:uchi@sco.bekkoame.ne.jp 28265
⡼ޥ
#28265
uchinyanء
ʤۤɡ
Ƥߤȡ錄Τ̷⤹뤫ʤäƤȤϸʤޤǤǤϤʤäƤȤͤ(^^;
꤬ȤޤOrZ
917 23:18:45 MAIL:crazy_tombo@yahoo.co.jp 28266
fumio
Ϥ褦ޤ
920ʿ 11:22:37 28269