In Mathematics
Fifty is the smallest number that is the sum of two non-zero square numbers in two distinct ways: 50 = 12 + 72 = 52 + 52. It is also the sum of three squares, 50 = 32 + 42 + 52. It is a Harshad number.
There is no solution to the equation φ(x) = 50, making 50 a nontotient. Nor is there a solution to the equation x − φ(x) = 50, making 50 a noncototient.
The aliquot sum of 50 is 43 and its aliquot sequence is (50,43,1,0). Fifty is itself the aliquot sum of 40 and 94.
Read more about this topic: 50 (number)
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“Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data ... and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.”
—Simone Weil (1909–1943)
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—Willard Van Orman Quine (b. 1908)