Records on Equal Sums of Like Powers

- Ideal non-negative integer solutions ( T/L = 150 types )
- Ideal integer solutions ( T/L = 57 types )
- Ideal prime solutions ( T/L = 23 types )

Type |
First solved in |
First solved by |

( k = 1 ) | ||

( k = 2 ) | ||

( k = 3 ) | ||

( k = 4 ) | 1772 | Euler |

( k = 1, 2 ) | ||

( k = 1, 3 ) | 1939 | A.Moessner |

( k = 1, 4 ) | 1995-02-08 | Chen Shuwen |

( k = 1, 5 ) | 1939 | A.Moessner |

( k = 2, 3 ) | 1949 | A.Golden |

( k = 2, 4 ) | ||

( k = 2, 6 ) | 1934 | Subba-Rao |

( k = 1, 2, 3 ) | 1910 | L.E.Dickson |

( k = 1, 2, 4 ) | 1995-02-24 | Chen Shuwen |

( k = 1, 2, 5 ) | 1995-10-20 | Chen Shuwen |

( k = 1, 2, 6 ) | 1995-04-22 | L.Lander, T.Parkin, J.Selfridge, Chen Shuwen |

( k = 1, 3, 4 ) | 1995-10-22 | Chen Shuwen |

( k = 1, 3, 5 ) | ||

( k = 1, 3, 7 ) | 1999 | Ajai Choudhry |

( k = 2, 3, 4 ) | 1995-11-15 | Chen Shuwen |

( k = 2, 4, 6 ) | 1913 | Crussol |

( k = 1, 2, 3, 4 ) | ||

( k = 1, 2, 3, 5 ) | 1995-04-09 | Chen Shuwen |

( k = 1, 2, 3, 6 ) | 1999-07-04 | Chen Shuwen |

( k = 1, 2, 4, 6 ) | 1953 | G.Palama |

( k = 1, 3, 5, 7 ) | 1940 | A.Golden |

( k = 2, 4, 6, 8 ) | 1940 | A.Letac |

( k = 1, 2, 3, 4, 5 ) | 1912 | G.Tarry |

( k = 1, 2, 3, 4, 6 ) | 1995-10-27 | Chen Shuwen |

( k = 1, 2, 3, 5, 7 ) | 1999-08-16 | Chen Shuwen |

( k = 1, 2, 4, 6, 8 ) | 1995-02-27 | Chen Shuwen |

( k = 1, 3, 5, 7, 9 ) | 2000-10-16 | Chen Shuwen |

( k = 2, 4, 6, 8, 10 ) | 1999-09-07 | Nuutti Kuosa, Jean-Charles Meyrignac, Chen Shuwen |

( k = 1, 2, 3, 4, 5, 6 ) | 1910 | E.B.Escott |

( k = 1, 2, 3, 4, 5, 7 ) | 1995-11-30 | Chen Shuwen |

( k = 1, 2, 3, 4, 5, 6, 7 ) | 1913 | G.Tarry |

( k = 1, 2, 3, 4, 5, 6, 8 ) | 1999-06-28 | Chen Shuwen |

( k = 1, 2, 3, 4, 5, 6, 7, 8 ) | 1940 | A.Letac |

( k = 1, 2, 3, 4, 5, 6, 7, 8, 9 ) | 1940 | A.Letac |

( k = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ) | 1999-09-07 | Nuutti Kuosa, Jean-Charles Meyrignac, Chen Shuwen |

( k = -1 ) | ||

( k = -2 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -3 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -4 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -3, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -4, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -5, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -3, -2 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -4, -2 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -6, -2 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -3, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -4, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -5, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -6, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -4, -3, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -5, -3, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -7, -3, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -4, -3, -2 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -6, -4, -2 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -4, -3, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -5, -3, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -6, -3, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -6, -4, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -7, -5, -3, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -8, -6, -4, -2 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -5, -4, -3, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -7, -5, -3, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -6, -4, -3, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -8, -6, -4, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -9, -7, -5, -3, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -10, -8, -6, -4, -2 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -6, -5, -4, -3, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -7, -5, -4, -3, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -7, -6, -5, -4, -3, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -8, -6, -5, -4, -3, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -8, -7, -6, -5, -4, -3, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -9, -8, -7, -6, -5, -4, -3, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -11, -9, -8, -7, -6, -5, -4, -3, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = 0 ) | ||

( k = 0, 1 ) | 1939 | A.Moessner |

( k = 0, 2 ) | Bini, Dubouis and Mathieu [49] | |

( k = 0, 3 ) | Stephane Vandemergel [49] | |

( k = 0, 4 ) | Stephane Vandemergel [49] | |

( k = 0, 1, 2 ) | 1944 | A.Golden |

( k = 0, 1, 3 ) | 2001-05-08 | Chen Shuwen |

( k = 0, 1, 4 ) | 2017-03-24 | Chen Shuwen |

( k = 0, 1, 5 ) | 2017-03-24 | Chen Shuwen |

( k = 0, 2, 4 ) | 2001-05-08 | Chen Shuwen |

( k = 0, 2, 6 ) | 2017-05-19 | Chen Shuwen |

( k = 0, 1, 2, 3 ) | 2000 | Guo Xianqiang |

( k = 0, 1, 2, 4 ) | 2017-03-22 | Chen Shuwen |

( k = 0, 1, 2, 6 ) | 2017-05-31 | Chen Shuwen |

( k = 0, 2, 4, 6 ) | 2017-03-21 | Chen Shuwen |

( k = 0, 1, 2, 3, 4 ) | 2001-03-29 | Chen Shuwen |

( k = 0, 1, 2, 3, 5 ) | 2017-04-15 | Chen Shuwen |

( k = 0, 1, 2, 4, 6 ) | 2017-03-23 | Chen Shuwen |

( k = 0, 1, 2, 3, 4, 5 ) | 2001-03-29 | Chen Shuwen |

( k = 0, 1, 2, 3, 4, 6 ) | 2017-05-26 | Chen Shuwen |

( k = 0, 1, 2, 3, 4, 5, 6 ) | 2001-03-29 | Chen Shuwen |

( k = -1, 0 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -2, 0 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -3, 0 ) | 2001-05-08 |
by Chen Shuwen's Theorem 9 |

( k = -4, 0 ) | 2001-05-08 |
by Chen Shuwen's Theorem 9 |

( k = -2, -1, 0 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( k = -3, -1, 0 ) | 2001-05-08 |
by Chen Shuwen's Theorem 9 |

( k = -4, -1, 0 ) |
2017-03-24 |
Chen Shuwen |

( k = -4, -2, 0 ) | 2001-05-08 |
by Chen Shuwen's Theorem 9 |

( k = -5, -1, 0 ) | 2017-03-24 | Chen Shuwen |

( k = -6, -2, 0 ) | 2017-05-19 | Chen Shuwen |

( k = -3, -2, -1, 0 ) | 2001 | Guo Xianqiang, Chen Shuwen |

( k = -4, -2, -1, 0 ) | 2017-03-22 | Chen Shuwen |

( k = -6, -2, -1, 0 ) | 2017-05-31 | Chen Shuwen |

( k = -6, -4, -2, 0 ) | 2017-03-21 | Chen Shuwen |

( k = -4, -3, -2, -1, 0 ) | 2001 | Guo Xianqiang, Chen Shuwen |

( k = -5, -3, -2, -1, 0 ) |
2017-04-15 |
Chen Shuwen |

( k = -6, -4, -2, -1, 0 ) |
2017-03-23 |
Chen Shuwen |

( k = -5, -4, -3, -2, -1, 0 ) | 2001-03-29 |
by Chen Shuwen's Theorem 9 |

( k = -6, -4, -3, -2, -1, 0 ) |
2017-05-26 |
Chen Shuwen |

( k = -6, -5, -4, -3, -2, -1, 0 ) | 2001-03-29 |
by Chen Shuwen's Theorem 9 |

( k = -1, 1 ) | 2001-05-06 | Chen Shuwen |

( k = -1, 2 ) | 2001-05-08 | Chen Shuwen |

( k = -2, 1 ) | 2001-05-08 | Chen Shuwen |

( k = -2, 2 ) | 2011 | Ajai Choudhry |

( k = -1, 0, 1 ) | 2001-05-08 | Guo Xianqiang |

( k = -1, 0, 2 ) | 2017-03-25 | Chen Shuwen |

( k = -1, 1, 2 ) | 2017-03-20 | Chen Shuwen |

( k = -1, 1, 3 ) | 2017-03-20 | Chen Shuwen |

( k = -1, 1, 5 ) | 2017-04-07 | Chen Shuwen |

( k = -2, 0, 1 ) | 2017-03-25 | Chen Shuwen |

( k = -2, 0, 2 ) | 2014-09-06 | Chen Shuwen |

( k = -2, -1, 1 ) | 2017-03-20 | Chen Shuwen |

( k = -3, 0, 3 ) | 2017-03-25 | Chen Shuwen |

( k = -3, -1, 1 ) | 2017-03-20 | Chen Shuwen |

( k = -5, -1, 1 ) | 2017-04-07 | Chen Shuwen |

( k = -1, 0, 1, 2 ) | 2017-03-22 | Chen Shuwen |

( k = -1, 0, 1, 3 ) | 2017-03-22 | Chen Shuwen |

( k = -2, 0, 2, 4 ) | 2017-05-31 | Chen Shuwen |

( k = -2, -1, 0, 1 ) | 2017-03-22 | Chen Shuwen |

( k = -2, -1, 1, 2 ) | 2017-03-30 | Chen Shuwen |

( k = -3, -1, 0, 1 ) | 2017-03-22 | Chen Shuwen |

( k = -4, -2, 0, 2 ) | 2017-05-31 | Chen Shuwen |

( k = -1, 0, 1, 2, 3 ) | 2017-03-22 | Chen Shuwen |

( k = -1, 0, 1, 2, 4 ) | 2017-05-26 | Chen Shuwen |

( k = -2, -1, 0, 1, 2 ) | 2017-03-29 | Chen Shuwen |

( k = -3, -1, 0, 1, 3 ) | 2017-03-30 | Chen Shuwen |

( k = -3, -2, -1, 0, 1 ) | 2017-03-22 | Chen Shuwen |

( k = -4, -2, -1, 0, 1 ) | 2017-05-26 | Chen Shuwen |

( k = -1, 0, 1, 2, 3, 4 ) | 2017-05-21 | Chen Shuwen |

( k = -4, -3, -2, -1, 0, 1 ) | 2017-05-21 | Chen Shuwen |

( k = -3, -2, -1, 0, 1, 2, 3 ) | 2017-03-30 | Chen Shuwen |

Type |
First solved in |
First solved by |

( h = 1, 2, 4 ) | ||

( h = 1, 2, 6 ) | 1997-05-11 | Chen Shuwen |

( h = 1, 3, 4 ) | 1991 | Ajai Choudhry |

( h = 2, 3, 4 ) | 2001 | Ajai Choudhry |

( h = 1, 2, 3, 5 ) | 1944 | A.Golden |

( h = 1, 2, 4, 6 ) | 1953 | G.Palama |

( h = 1, 2, 3, 4, 6 ) | 1944 | A.Golden |

( h = 1, 2, 3, 5, 7 ) | 1953 | G.Palama |

( h = 1, 2, 4, 6, 8 ) | 1940 | A.Letac |

( h = 1, 2, 3, 4, 5, 7 ) | 1944 | A.Golden |

( h = 1, 2, 3, 5, 7, 9 ) | 2000-10-16 | Chen Shuwen |

( h = 1, 2, 4, 6, 8, 10 ) | 1999-09-08 | Nuutti Kuosa, Jean-Charles Meyrignac, Chen Shuwen |

( h = 1, 2, 3, 4, 5, 6, 8 ) | 1997-05-19 | Chen Shuwen |

( h = 1, 2, 3, 4, 5, 6, 7, 9 ) | 1997-05-19 | Chen Shuwen |

( h = -4, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( h = -6, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( h = -4, -3, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( h = -4, -3, -2 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( h = -5, -3, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( h = -6, -4, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( h = -6, -4, -3, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( h = -7, -5, -3, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( h = -8, -6, -4, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( h = -7, -5, -4, -3, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( h = -9, -7, -5, -3, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( h = -10, -8, -6, -4, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( h = -8, -6, -5, -4, -3, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( h = -9, -7, -6, -5, -4, -3, -3, -2, -1 ) | 2001-03-26 |
by Chen Shuwen's Theorem 9 |

( h = 0, 1, 3 ) | 1939 | A.Moessner |

( h = 0, 1, 2, 4 ) | 2011 | Ajai Choudhry |

( h = 0, 1, 3, 5 ) | 2017-03-26 | Chen Shuwen |

( h = 0, 1, 2, 3, 5 ) | 2011 | Ajai Choudhry |

( h = 0, 1, 2, 4, 6 ) | 2017-03-21 | Chen Shuwen |

( h = 0, 1, 2, 3, 4, 6 ) | 2011 | Ajai Choudhry |

( h = -3, -1, 0 ) |
2001-03-26 |
by Chen Shuwen's Theorem 9 |

( h = -4, -2, -1, 0 ) | 2011 |
by Chen Shuwen's Theorem 9 |

( h = -5, -3, -1, 0 ) |
2017-03-26 |
Chen Shuwen |

( h = -5, -3, -2, -1, 0 ) | 2011 |
by Chen Shuwen's Theorem 9 |

( h = -6, -4, -2, -1, 0 ) |
2017-03-21 |
Chen Shuwen |

( h = -6, -4, -3, -2, -1, 0 ) | 2011 |
by Chen Shuwen's Theorem 9 |

( h = -1, 0, 2 ) | 2017-03-26 | Chen Shuwen |

( h = -1, 1, 2 ) | 2011 | Ajai Choudhry |

( h = -2, 0, 1 ) | 2017-03-26 | Chen Shuwen |

( h = -2, -1, 1 ) |
2011 |
by Chen Shuwen's Theorem 9 |

( h = -1, 0, 1, 3 ) | 2017-03-26 | Chen Shuwen |

( h = -1, 0, 1, 5 ) | 2017-04-07 | Chen Shuwen |

( h = -1, 1, 2, 3 ) | 2011 | Ajai Choudhry |

( h = -2, 0, 1, 2 ) | 2017-03-25 | Chen Shuwen |

( h = -2, -1, 0, 2 ) | 2017-03-25 | Chen Shuwen |

( h = -2, -1, 1, 2 ) | 2011 | Ajai Choudhry |

( h = -3, -1, 0, 1 ) |
2017-03-26 |
Chen Shuwen |

( h = -3, -2, -1, 1 ) |
2011 |
by Chen Shuwen's Theorem 9 |

( h = -5, -1, 0, 1 ) |
2017-04-07 |
Chen Shuwen |

( h = -1, 0, 1, 2, 3, 5 ) |
2017-03-27 |
Chen Shuwen |

( h = -1, 1, 2, 3, 4, 5 ) |
2011 |
Ajai Choudhry |

( h = -5, -3, -2, -1, 0, 1 ) |
2017-03-27 |
Chen Shuwen |

( h = -5, -4, -3, -2, -1, 1 ) | 2011 |
by Chen Shuwen's Theorem 9 |

( k = 1 ) | ||

( k = 2 ) | 2000-09-08 | Jean-Charles Meyrignac |

( k = 3 ) | 2000-09-08 | Jean-Charles Meyrignac |

( k = 4 ) | 2000-09-03 | Jean-Charles Meyrignac |

( k = 1, 2 ) | 1964 | Albert H. Beiler |

( k = 1, 3 ) | 2016-09-26 | Chen Shuwen |

( k = 1, 4 ) | 2016-09-25 | Chen Shuwen |

( k = 1, 5 ) | 2002-01-03 | Jaroslaw Wroblewski |

( k = 2, 4 ) | 2016-09-25 | Chen Shuwen |

( k = 2, 6 ) | 2016-10-17 | Aloril, Jean-Charles Meyrignac, Chen Shuwen |

( k = 1, 2, 3 ) | 1964 | Albert H. Beiler |

( k = 1, 2, 4 ) | 2017-03-12 | Chen Shuwen |

( k = 1, 3, 5 ) | 2016-09-25 | Torbjorn Alm, Jean-Charles Meyrignac, Chen Shuwen |

( k = 2, 4, 6 ) | 2017-03-14 | Chen Shuwen |

( k = 1, 2, 3, 4 ) | 2016-09-26 | Chen Shuwen |

( k = 1, 2, 3, 5 ) | 2016-03-12 | Chen Shuwen |

( k = 1, 2, 4, 6 ) | 2017-03-15 | Chen Shuwen |

( k = 1, 3, 5, 7 ) | 1999 | Carlos Rivera |

( k = 1, 2, 3, 4, 5 ) | 1999-08-31 | T.W.A. Baumann |

( k = 1, 2, 3, 4, 5, 6 ) | 2016 | Qiu Min, Wu Qiang |

( k = 1, 2, 3, 4, 5, 6, 7 ) | 1999-09-01 | T.W.A. Baumann |

( k = 1, 2, 3, 4, 5, 6, 7, 8 ) | 2016-09-30 | Chen Shuwen |

( k = 1, 2, 3, 4, 5, 6, 7, 8, 9 ) | 2016-10-04 | Chen Shuwen |

Copyright 1997-2017, Chen Shuwen