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In article <220@okds1.osaka-kyoiku.ac.jp> koshi@okds1.uucp (Kunio Koshigiri) writes:

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In article <NAGAE.92Sep11142606@momo.an.isl.titech.ac.jp>
nagae@an.isl.titech.ac.jp (Takanori Nagae) writes:

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In article <NAGAE.92Sep11142606@momo.an.isl.titech.ac.jp> nagae@an.isl.titech.ac.jp writes:
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-- 
=================================== $@0f>e9@0l!wBg:eI\N)9b@l(J=====================
                   Phone : (0720) 21-6401 ($@Fb@~(J304)  Fax : (0720) 21-0134
                   E-mail: f51323@sakura.kudpc.kyoto-u.ac.jp
==============================================$@;d$O(Jmohta$@;a$K5wN%$r$*$-$^$9!#(J====

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In article <NAGAE.92Sep11142606@momo.an.isl.titech.ac.jp> nagae@an.isl.titech.ac.jp writes:
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-- 
=================================== $@0f>e9@0l!wBg:eI\N)9b@l(J=====================
                   Phone : (0720) 21-6401 ($@Fb@~(J304)  Fax : (0720) 21-0134
                   E-mail: f51323@sakura.kudpc.kyoto-u.ac.jp
==============================================$@;d$O(Jmohta$@;a$K5wN%$r$*$-$^$9!#(J====

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In article <1992Sep12.063153.18984@kudpc.kyoto-u.ac.jp> f51323@sakura.kudpc.kyoto-u.ac.jp (inoue kouichi) writes:
>  $BA0%]%9%H$r$7$?$"$H$G!"<+J,$J$j$K$$$m$$$m9M$($F$_$^$7$?$,!"$I$&$b463P(J
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$B$3$l$h$j!"$D$.$N#2$D$N>r7o$,$($i$l$^$9!#(J
 B = Sqrt[n] (n:integer) $B!((J $B&H(J = ArcCos[m/Sqrt[4*n]] (m:integer)
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$BC10L3J;R$KBP$9$kLL@QHf(J)$B$O!"(JAbs[ i + j *B*Exp[I$B&H(J] ] ^2 = 
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 kousi[n_,m_]:= 
 Take[Union[Flatten[Table[i^2 + m i*j + n j^2,{i,0,16},{j,0,16}]]],16]

Do[Print[kousi[n,0]],{n,1,4}]
{0, 1, 2, 4, 5, 8, 9, 10, 13, 16, 17, 18, 20, 25, 26, 29}   --> Quiz 1
{0, 1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 17, 18, 19, 22, 24}  
{0, 1, 3, 4, 7, 9, 12, 13, 16, 19, 21, 25, 27, 28, 31, 36}  --> Quiz 2
{0, 1, 4, 5, 8, 9, 13, 16, 17, 20, 25, 29, 32, 36, 37, 40}

Do[Print[kousi[n,1]],{n,1,4}]
{0, 1, 3, 4, 7, 9, 12, 13, 16, 19, 21, 25, 27, 28, 31, 36}  --> Quiz 2
{0, 1, 2, 4, 8, 9, 11, 14, 16, 18, 22, 23, 25, 28, 32, 36}
{0, 1, 3, 4, 5, 9, 12, 15, 16, 20, 23, 25, 27, 31, 33, 36}
{0, 1, 4, 6, 9, 10, 16, 19, 24, 25, 31, 34, 36, 40, 46, 49}

$BLdBj$,$I$s$I$s$G$-$k!&!&!&!!(J*_*;;

K. Koshigiri
koshi@cc.osaka-kyoiku.ac.jp

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In article <1992Sep12.030706.18358@kudpc.kyoto-u.ac.jp> f51323@sakura.kudpc.kyoto-u.ac.jp (inoue kouichi) writes:

>In article <NAGAE.92Sep11142606@momo.an.isl.titech.ac.jp> nagae@an.isl.titech.ac.jp writes:
>>$@$3$l$O$^$5$K!$Fs<!(J$@$N@0?t$N%$%G%"%k$NOC$G$9$M!%(J
>>$@3J;R>e3J;R$,C10L3J;R$HAj;w$K$J$k$N$OC19`%$%G%"%k$N$H$-!$$D$^$j!$G\?t$K(J
>
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  H = GM           ...(1)

$@$,@.$jN)$A$^$9!%$^$?(J$@!$(JH$@$,I=$93J;R$,(JG$@$,I=$93J;R$KAj;w$G$"$k$H$-$K$O!$Aj(J
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$@$N9TNs(J($@$3$l$r(Junimodular matrix$@$H$$$&$i$7$$(J)U$@$,$"$C$F!$(J

  H = SGU          ...(2)

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  G = SGM          ...(3)

$@$,F@$i$l$^$9(J($@C"$7!$(JS^{-1}$@$r?7$?$K(JS$@$H$*$-(J$@!$(JMU^{-1}$@$r?7$?$K(JM$@$H$*$$$F$$$k(J)$@!%(J
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       m_1  m_2
 M = (          )  ...(4)
       m_3  m_4
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 x^2 - (m_1 + m_4)x + (m_1m_4 - m_2m_3) = 0,           ...(5)
 $@H=JL<0(J: D = (m_1 + m_4)^2 - 4(m_1m_4 - m_2m_3) < 0.   ...(6)

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In article <TACCHAN.92Sep11160912@topor.soft.flab.fujitsu.co.jp> tacchan@flab.fujitsu.co.jp (Tatsuo KONDO) writes:

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>Plane Geometry and Number Theory $@!J=PHG$O(J Mathematical Association of
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