Sunday, September 18, 2011

Beautiful Number Relationship

Notice the consecutive exponents.
135 = 11 + 32 + 53
175 = 11 + 72 + 53
518 = 51 + 12 + 83
598 = 51 + 92 + 83

Now, take it to one place further.
1306 = 11 + 32 + 03 + 64
1676 = 11 + 62 + 73 + 64
2427 = 21 + 42 + 23 + 74

The next ones are really amazing.
Notice the relationship between the exponents and the numbers.
3435 = 33 + 44 + 33 + 55
438579088 = 44 + 33 + 88 + 55 + 77 + 99 + 00 + 88 + 88
(We’ve considered here 00 as 0. But, in fact, it’s undetermined.)

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