## multigradeSets of equations in which the sums of powers of two different sets of numbers are the same for several different exponents. The simplest example is: 1 + 6 + 8 = 2 + 4 + 9Another multigrade is: 1 + 8 + 10 + 17 = 36 = 2 + 5 + 13 + 16Remarkably, if any integer is added to all the terms of a multigrade it will still hold. Adding 1 to the example above, gives the multigrade (2, 9, 11, 18); (3, 6, 14, 17) (n = 1,2,3). Some high-order multigrades include: (1, 50, 57, 15, 22, 71); (2, 45, 61, 11, 27, 70); (5, 37, 66, 6, 35, 67) ( ## Related category• NUMBER THEORY | |||||

Home • About • Copyright © The Worlds of David Darling • Encyclopedia of Alternative Energy • Contact |