Mixed power relations-2
The sum of four different power of any successive four numbers has shown yet another regularity in its structure.
1 + 22 + 33 + 44 = 288 = 3 x 42 x 6
2 + 32 + 43 + 54 = 700 = 4 x 52 x 7
3 + 42 + 53 + 64 = 1440 = 5 x 62 x 8
4 + 52 + 63 + 74 = 2646 = 6 x 72 x 9
5 + 62 + 73 + 84 = 4480 = 7 x 82 x 10
In general this can be expressed as
(x-3) + (x-2)2 + (x- 1)3 + x4 = (x-1) x2 (x+2)
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