In Mathematics
32 is the smallest number n with exactly 7 solutions to the equation φ(x) = n. It is also the sum of the totient function for the first ten integers.
The fifth power of two, 32 is also a Leyland number since 24 + 42 = 32.
As with every power of two, 32 has an aliquot sum one less than itself: the prime 31. 32 is the first member of the 31-aliquot tree.
32 is the ninth happy number.
32 = 11 + 22 + 33
Read more about this topic: 32 (number)
Famous quotes containing the word mathematics:
“Why does man freeze to death trying to reach the North Pole? Why does man drive himself to suffer the steam and heat of the Amazon? Why does he stagger his mind with the mathematics of the sky? Once the question mark has arisen in the human brain the answer must be found, if it takes a hundred years. A thousand years.”
—Walter Reisch (1903–1963)
“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)