Re: [Q] a Diophantine Equation

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Article #13871

#13871

From: FUJITA Hiroshi
Date: Fri, 12 Apr 1996 00:00

22 lines
1451 bytes

$B:FEY<+8J%U%)%m!<$7$^$9(B. $BF#ED$G$9(B.

x^2 + y^2 = 3 $B$KM-M}?t2r$N$J$$$3$H$N>ZL@$G$9(B. $B$G$-$F$7(B
$B$^$($P(B, $B0U30$H4JC1$G$7$?(B. 

  a^2 + b^2 = 3c^2 (mod 4)

$B$H2>Dj$7$F(B, $B$7$+$b(B a,b,c $B$N#3$D$H$b$K6&DL$N0x?t$O$J$$$H(B
$B2>Dj$G$-$k(B. $B4q?t$NJ?J}$O(B mod 4 $B$G(B 1, $B6v?t$NJ?J}$O(B mod 4 
$B$G(B 0 $B$J$N$G(B, $B:8JU$O(B mod 4 $B$G(B 3 $B$K$J$k$3$H$O$J$$(B. $B$3$N$3(B
$B$H$+$i(B, c^2 $B$O(B mod 4 $B$G(B 0, $B$D$^$j(B c $B$O6v?t(B. $B$H$3$m$,(B, 
a^2 + b^2 $B$,(B mod 4 $B$G(B 0 $B$K$J$k$N$O(B, a $B$H(B b $B$NN>J}$,6v?t(B
$B$K$J$k>l9g$@$1$@$+$i(B, a, b, c $B$K6&DL$N0x?t$,$J$$$H8@$&(B
$B2>Dj$KL7=b$9$k(B. 

----------------------------------------------------------
$BF#ED(B  $BGn;J(B (FUJITA Hiroshi)
fujita@dpc.ehime-u.ac.jp
$B0&I2Bg3XM}3XIt?tM}2J3X2J!Z")(B790 $B>>;3;TJ85~D.(B2-5$B![(B

 *** $B0&I2Bg3XM}3XIt?t3X2J$O(B $B?tM}2J3X2J(B $B$KJQ$o$j$^$7$?(B ***
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X-Google-Language: Japanese,JIS
X-Google-Thread: f4956,90ad3e8c68ab1fc8
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From: fujita@dpc.ehime-u.ac.jp (FUJITA Hiroshi)
Subject: Re: [Q] a Diophantine Equation
Date: 1996/04/12
Message-ID: <4kkvvo$cpa@doc.dpc.ehime-u.ac.jp>
X-Deja-AN: 147072884
references: <4kkhr2$9e3@doc.dpc.ehime-u.ac.jp>
organization: Ehime University, Japan
newsgroups: fj.sci.math

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