Multigrade Equation
A 
-multigrade equation is a Diophantine Equation of the form
for
, ..., 
, where m and n are 
-Vectors. Multigrade identities remain valid if aconstant is added to each element of m and n (Madachy 1979), so multigrades can always be put in a form where theminimum component of one of the vectors is 1.Small-order examples are the (2, 3)-multigrade with
and 
:
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the (3, 4)-multigrade with
and 
: | |  | |
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and the (4, 6)-multigrade with
and 
: | |  | |
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(Madachy 1979).
A spectacular example with 
and 
is given by 
and
(Guy 1994), which has sums
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See also Diophantine Equation
References
Chen, S. ``Equal Sums of Like Powers: On the Integer Solution of the Diophantine System.'' http://www.nease.net/~chin/eslp/ Gloden, A. Mehrgeradige Gleichungen. Groningen, Netherlands: Noordhoff, 1944. Gloden, A. ``Sur la multigrade Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 143, 1994. Kraitchik, M. ``Multigrade.'' §3.10 in Mathematical Recreations. New York: W. W. Norton, p. 79, 1942. Madachy, J. S. Madachy's Mathematical Recreations. New York: Dover, pp. 171-173, 1979.
, 
, 
, 
, 
, 
, 
, 
, 
(
, 3, 5, 7).'' Revista Euclides 8, 383-384, 1948.
- Hadamard Design
- Hadamard Matrix
- Hadamard's Inequality
- Hadamard's Theorem
- Hadamard Transform
- Hadamard-Vallée Poussin Constants
- Hadwiger Problem
- Hadwiger's Principal Theorem
- Hafner-Sarnak-McCurley Constant
- Hahn-Banach Theorem
- Hailstone Number
- Hairy Ball Theorem
- Half
- Half-Closed Interval
- Half-Normal Distribution
- Half-Open Interval
- Halley's Irrational Formula
- Halley's Method
- Halley's Rational Formula
- Hall-Janko Group
- Halphen Constant
- Halphen's Transformation
- Halting Problem
- Hamiltonian Circuit
- Hamiltonian Cycle