computer number theory

Computational Number Theory

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Update 2012.2.1

New!

           [128. Equal sums and equal products    (2012.2.1)]
           [127. Happy New Year!    (2012.1.3)]
           [126. Any non-zero rational number m is the sum of three rational cubes
               in an infinite number of non-trivial ways.  (2011.12.6)]
           [125. New parametric solutions of x^3 + y^3 + z^3 = t^2  (2011.11.16)]
           [124. Equal Sums of Eighth Powers et 1  (2011.10.11)]
           [123. Equal Sums of Fourth Powers et 1  (2011.9.13)]
           [122. Equal Sums of Fifth Powers et 1  (2011.8.23)]
           [121. Equal Sums of Sixth Powers et 1  (2011.8.1)]
           [120. Equal Sums of Seventh Powers et 1  (2011.7.18)]
           [119. Equal Sums of Eighth Powers   (2011.7.1)]
           [118. Solutions  of  x^4 + y^4 + z^4 = w^n   (2011.6.3)]
           [117. EQUAL SUMS OF ELEVENTH POWERS   (2011.5.6)]
           [116. Solutions  of  x^4 + y^4 + z^4 = nw^3   (2011.4.1)]
           [115. EQUAL SUMS OF SEVENTH POWERS   (2011.3.4)]
           [114. New solution:  3047 =  234115946^3  -  81713665^3 - 2* 183146068^3  (2011.2.16)]
           [113. Generalized Taxicab Number Part 2  (2011.2.1)]
           [112. Happy New Year!    (2011.1.1)]
           [111. Generalized Taxicab Number   (2010.12.3)]
           [110. x₁^4 + x₂^4 +...+ x_n^4 = nw^2  (2010.11.1)]
           [109. ON EQUAL SUMS OF NINTH POWERS  Part 2  (2010.10.1)]
           [108. Solutions  of  x^4 + y^4 + z^4 = nw^2  (2010.9.1)]
           [107. Any rational number N is the sum and difference of four rational fourth powers
               in an infinite number of ways.  (2010.8.1)]
           [106. ON EQUAL SUMS OF NINTH POWERS  (2010.7.20)]
           [105. Solutions  of  x^4 + y^4 = cz^2  (2010.8.6)(2010.8.5)(2010.7.1)]
           [104. Solutions  of  X^3 + Y^3 + Z^3 = mW^3  (2010.6.1)]
           [103. 3956=    3481598477^3  -  1323591649^3 - 2*  2711779804^3  (2010.5.11)]
                8779=   64325766916^3  - 11325451823^3 - 2* 50962343435^3
          [102. Solutions  of  x³ + y³ + z³ = tⁿ  (2010.5.1)]
          [101. A⁴+ B⁴+ C⁴ = D⁴+ E⁴  Part 2  (2010.4.10)]
          [91.　Solutions of a^4 + b^4 + c^4 + d^4 = (a+b+c+d)^4    (2010.4.11)(2010.4.7)(2010.4.2)(2009.7.30)(2009.7.12)]
          [100. x^4 + ay^4 = z^4 + bt^4 (2010.3.31)]
          [99.　1 = (4x^4 + 1)^4 -(4x^4)^4 -(4x^3)^4 -(2x)^4 -(3x^2)^4 -(2x^2)^4 +(x^2)^4 (2010.3.26)]
          [98.　2 = (8x^5-2x)^4 + (8x^4+1)^4 + (8x^4-1)^4 - (8x^5+2x)^4 - (4x^2)^4 (2010.3.10)]
          [97.　Ramanujan's identity (4x^5-5x)^4 + (6x^4-3)^4 + (4x^4+1)^4 - (4x^5+x)^4 - (2x^4-1)^4 = 81 (2010.3.3)]
          [70.　Solutions  of  a1⁵+a2⁵+a3⁵ = b1⁵+b2⁵+b3⁵   (2010.2.12) (2008.5.1)]
          [96.　Repunit    (2010.1.13)]
          [95.　A Happy New Year!    (2010.1.1)]
          [94.　On factors of Mersenne numbers.    (2009.12.10)]
          [93.　Solutions  of  X⁴ + Y⁴ = 4481Z².    (2009.11.1)]
          [92.　Smallest number that is a sum of two n-th powers of positive
              rationals but not of two n-th powers of positive integers.  (2009.9.6)]
          [91.　Solutions of a^4 + b^4 + c^4 + d^4 = (a+b+c+d)^4    (2009.7.30)(2009.7.12)]
          [90.　Solutions  of  a1⁶+a2⁶+a3⁶ = b1⁶+b2⁶+b3⁶    (2009.6.26)]
          [89.　Representation by fourth powers  Part 2    (2009.6.15)]
          [88.  9033964577482532388059482429398457291004947925005743028147465732645880^4 +
               4417264698994538496943597489754952845854672497179047898864124209346920^4 +
               1439965710648954492268506771833175267850201426615300442218292336336633^4 =
               9161781830035436847832452398267266038227002962257243662070370888722169^4  (2009.6.1)]
          [87.　Representation by fourth powers     (2009.5.1)]
          [86.　A⁴+ B⁴+ C⁴+ D⁴+ E⁴= F⁴ (Ramanujan's identities, again x 2)  (2009.3.16)]
          [85.　x⁴+y⁴+z⁴ = nw⁴    (2009.3.1)]
          [84.　A⁴=B⁴+C⁴+D⁴+E⁴    (2009.2.10)]
          [83.　A Happy New Year!    (2009.1.1)]
          [82.　Table of the solutions for x³+by³+cz³=0.  (2008.12.3)]
          [81.　Every integer is a sum of four cubes of integers?  (2008.11.1)]
          [80.　Table of the solutions for A⁴+B⁴+C⁴=D⁴  Part 2  (2008.10.5)]
          [79.　130064300991400⁴+ 440804942580160⁴+ 514818101299289⁴= 573646321871961⁴  (2008.9.15)]
          [78.　Table of the solutions for A⁴+B⁴+C⁴=D⁴  (2008.9.1)]

          [77.　1259768473⁴=1166705840⁴+859396455⁴+588903336⁴  (2008.9.1)]
                 873822121⁴=769321280⁴+606710871⁴+558424440⁴
              1787882337⁴=1662997663⁴+1237796960⁴+686398000⁴
              1871713857⁴=1593513080⁴+1553556440⁴+92622401⁴

          [76.　47886740272114976⁴ + 8813425670440240⁴ + 56827813308111785⁴ = 62940516903410601⁴  (2008.8.13)]
               3579087147375440⁴ +14890026433468471⁴ + 18565945114216720⁴ = 20249506709579721⁴  (2008.8.13)]
          [75.　New solutions of n=x³+y³+2z³  (2009.1.15)(2008.7.31)(2008.7.13)(2008.6.22)]
          [74.　Solve the Diophantine equation like Diophantus    (2008.6.15)]
          [73.　N=5,6,and 7 mod 8 is always a congruent number    (2008.6.1)]
          [72.　4987588419655⁴+2480452675600⁴+502038853976⁴=5062297699257⁴    (2008.5.15)]
          [71.　4 + 27 = 31!?    (2008.5.12)]
          [70.　Solutions  of  a1⁵+a2⁵+a3⁵ = b1⁵+b2⁵+b3⁵    (2008.5.1)]
          [69.　Sierpinski problem    (2008.4.11)]
          [68.　Sums of three cubes    (2008.2.7)(2008.1.15)(2008.1.8)(2008.1.5)]

          [67.　A Happy New Year!    (2008.1.1)]
          [66.　5821981400⁴+15355831360⁴+140976551⁴=15434547801⁴  (2007.10.24)]
          [65.　A₁⁶+ A₂⁶+ ....+ A₆⁶ = B₁⁶+ B₂⁶+ ....+ B₆⁶        (2007.10.15)]
          [64.　A₁⁶+ A₂⁶+ ....+ A₅⁶ = B₁⁶+ B₂⁶+ ....+ B₅⁶        (2007.10.15)]
          [63.　EQUAL SUMS OF SEVENTH POWERS        (2007.8.20)(2007.10.15)]

テーマ
リンク集

1.　x³+y³+z³＝ｄ　の問題　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　続く　　　　　　　　　　　　　　

2.　素数を生成する３次多項式(2005.4.10)　　　

3.　x³+y³+z³＝w³のパラメータ解(2005.4.26)　　　

4.　ガウス讃、或いは温故知新(2005.5.5)　　　　　

5.　Demjanenko的恒等式(2005.5.10)

6.　オイラー敗れたり！(2005.5.22)(2005.6.13)

7.　インド人もビックリ！？(2005.6.16)

8.　続インド人もビックリ！？(2005.6.19)

9.　A⁴+B⁴+C⁴ = D⁴+E⁴+F⁴ 　(2005.6.25)

10.　続A⁴+B⁴+C⁴ = D⁴+E⁴+F⁴ 　(2005.7.15)

11.　和の世界　(2005.7.17)

12.　A⁵+B⁵+C⁵ = D⁵+E⁵+F⁵ 　(2005.8.14)

13. ＵＢＡＳＩＣ超入門　(2005.8.18)

14. ５乗数的有楽　(2005.8.21)

15. タクシーナンバーと楕円曲線　(2005.9.25)

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