Beautiful Number Relationships

Who said numbers can't form beautiful relationship! Look at these unique situations which might give you the feeling that there is more to "numbers" than meet the eyes.

Notice the consecutive exponents.

135 = 11 + 32 + 53
175 = 11 + 72 + 53
518 = 51 + 12 + 83
598 = 51 + 92 + 83

Now, taken one place further, we get

1,306 = 11 + 32 + 03 + 64
1,676 = 11 + 62 + 73 + 64
2,427 = 21 + 42 + 23 + 74

The next ones are really amazing. Notice the relationship between the exponents and the numbers.

3,435 = 33 + 44 + 33 + 55

438,579,088 = 44 + 33+ 88 + 55 + 77 + 99 + 00+ 88 + 88

Notice that, in the second illustration, for convenience and for the sake of this unusual situation, we have considered 00 as though its value is 0, when, in fact, it is indeterminate.

Here is a different one,

1,741,725 = 17 + 77 + 47 + 17 + 77+ 27 + 57


Yet another one,
Beautiful-number-relationship




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