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Unless some other LHS value is shown, each identity equates to [1], i.e. PI/4 (see the 'Identity lists' page for a full description of how identities are displayed).

4-TERM IDENTITIES (last updated 28 Sep 09)

Note: In this context, all four cotangent values must be integers

1.58604  STØRMER (1896)     (¢¢2.30154,¢¢2.37598,¢¢2.38268)
   44[57]+7[239]-12[682]+24[12943]
  Eliminated:{A}[11]

1.63435  ESCOTT (1896)
   22[28]+2[443]-5[1393]-10[11018]
  Eliminated:[2][14]([28])

1.71075  ARNDT (1993)
   17[23]+8[182]+10[5118]+5[6072]
  Eliminated:[2][12&104]([23])

1.75032  MRW (1980)         (*1.86105)
   16[21]+3[239]+4[347]-4[361577]
  Eliminated:[4][5]([347])

1.77990  TAKANO (1982)      (¢¢2.37598)
   12[49]+32[57]-5[239]+12[110443]
  Eliminated:{A}([49])

1.79645  MATSUMOTO (1996)   (*1.86105)
   16[21]+3[239]+4[343]-4[27493]
  Eliminated:[2&19][4][5]

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1.79992  ASN (29Jun09)      (*1.86105)
   16[21]+3[239]+4[353]+4[21637]
  Eliminated:[4][5]([353])

1.80943  CASTELLANOS (1988) (*1.94191)
   12[15]-[239]-4[433]+4[1875333]
  Eliminated:{A}([15][433])

1.81330  MRW (1980)
   17[22]+3[172]-2[682]-7[5357]
  Eliminated:[2][11]([22])

1.82119  MRW (1980)
   16[21]+7[239]-4[616]+4[3141]
  Eliminated:[4][5][10]
Cf. 2-digit identity with measure 1.71068

1.83520  ARNDT (1993)
   16[20]-[239]-4[515]-8[4030]
  Eliminated:[5][10]({20])

1.84407  ARNDT (1993)
   24[53]+20[57]-5[239]+12[4443]
  Eliminated:{A}([53])

1.85102  MRW (23Jun09)      (¢¢2.64766)
   24[29]-4[57]+7[239]-12[12238]
  Eliminated:{A}
N.B. 2[29]-[12238] = [29/2]; measure calculated accordingly.
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1.85423  ARNDT (1993)
   12[18]+8[109]+11[239]-8[6826318]
  Eliminated:{A}([109])

1.86105  ARNDT (1993)
   16[21]+3[239]+4[421]+4[1985]
  Eliminated:[4][5][20]
(v. derivations above, & 5-term 2-digit identity (1.74096))

1.88483  HCL (28Sep93)      (*1.89498)
   17[26]+5[38]+3[2682]-7[8827]
  Eliminated: [2][4]([26])

1.89498  ARNDT (1993)
   17[26]+5[38]+3[2057]-10[8827]
  Eliminated:[2][4]([26])

1.91841  ARNDT (1993)
   24[29]-4[57]+7[239]-12[12238]
  Eliminated:{A}([29])

1.94191  CASTELLANOS (1988)
   12[15]-[239]-4[580]-4[1710]
  Eliminated:[2&107][5]([15])

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1.96468  CASTELLANOS (1988)
   8[10]-[239]-8[1020]+4[52525]
  Eliminated:[5]([10][1020])

1.96806  HCL (26Jan95)      (*2.12025)
   12[18]+8[75]+3[239]+8[39307]
  Eliminated:{A}[12&22]

1.97678  ARNDT (1993)
5[1]=44[11]-9[239]-16[682]-12[12943]
  Eliminated:{A}([11])

1.99851  HCL (26Jan95)      (*2.05885)
   12[26]+20[57]-5[239]-12[2057]
  Eliminated:{A}([26]}

2.01918  ARNDT (1993)
   20[57]+24[68]+12[117]-5[239]
  Eliminated:{A}[6]

2.03480  GAUSS (1876)
   12[38]+20[57]+7[239]+24[268]
  Eliminated:{B}

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2.04205  ARNDT (1993)       (*2.12025)        
   12[18]+8[73]+3[239]-8[2943]
  Eliminated:{A}[9]

2.05885  ARNDT (1993)
   12[28]+20[57]-5[239]+12[443]
  Eliminated:{A}([28])

2.06116  KOEPP (1994)
   7[8]-4[47]+2[247057]-[740943]
  Eliminated:[2][4][5&114]

2.12025  LEHMER (1938)      (*2.24178)
   12[18]+8[99]+3[239]+8[307]
  Eliminated:{A}[12]

2.12663  ARNDT (1993)
2[1]=11[7]+4[443]+[1393]+2[11018]
  Eliminated:[2][14][28]

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2.17433  STØRMER (1896)
   10[22]+7[41]+12[75]+2[4193]
  Eliminated:[2][12]([22])

2.24178  BENNETT (1925)
   12[18]+3[70]+5[99]+8[307]
  Eliminated:{A}[12]

2.28539  STØRMER (1896)
   12[17]+3[57]+5[99]-7[307]
  Eliminated:{A}[12]

2.52115  ARNDT (1993)
   10[17]+2[38]+7[41]-4[157]
  Eliminated:{C -5}
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