Multigrade Equation

Author

Eric W. Weisstein
March 1, 2009

This notebook downloaded from http://mathworld.wolfram.com/notebooks/DiophantineEquations/MultigradeEquation.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/MultigradeEquation.html.

©2009 Wolfram Research, Inc. except for portions noted otherwise

Formulas

multi[n_List,j_]:=Sum[n[[i]]^j,{i,Length[n]}]
Multigrade[m_List,n_List,k_]:=Module[{m1,n1,j},
		m1=Table[multi[m,j],{j,k}];
    n1=Table[multi[n,j],{j,k}];
		{m1,m1-n1}
]

Multigrade[{1,6,8},{2,4,9},2]

Multigrade[{1,5,8,12},{2,3,10,11},3]

Multigrade[{1,5,8,12,18,19},{2,3,9,13,16,20},4]

m0={12,11881,20231,20885,23738};
n0={436,11857,20449,20667,23750};
Multigrade[Join[-m0,m0],Join[-n0,n0],9]

Gloden

Multigrade[{3,19,37,51,53},{9,11,43,45,55},7]

Multigrade[{1,33,39,65,71},{11,15,53,57,73},7]

Sinha

Subtract@@@Table[{(-7m^2+62m n-30n^2)^k+(7m^2+38m n-50n^2)^k
+(5m^2-8m n-22n^2)^k+(19m^2-32m n-42n^2)^k
+(-19m^2+36m n-62n^2)^k,(-9m^2+66m n-42n^2)^k+(5m^2+42m n-62n^2)^k
+(-21m^2+38m n-22n^2)^k+(9m^2-14m n-50n^2)^k
+(21m^2-36m n-30n^2)^k},{k,{1,3,5,7}}]//Expand