In Mathematics
91 is the twenty-seventh distinct semiprime and the second of the form (7.q). The aliquot sum of 91 is 21 within the aliquot sequence (91,21,11,1,0) 91 being the fourth composite number in the 11-aliquot tree.
91 is a triangular number and a hexagonal number, one of the few such numbers to also be a centered hexagonal number, and it is also a centered nonagonal number and a centered cube number. It is a square pyramidal number, being the sum of the squares of the first six integers.
91 is the smallest positive integer expressible as a sum of two cubes in two different ways if negative roots are allowed (alternatively the sum of two cubes and the difference of two cubes): 91 = 63+(-5)3 = 43+33. (See 1729 for more details). This implies that 91 is the second cabtaxi number.
91 is the smallest positive integer expressible as a sum of six distinct squares: 91 = 12+22+32+42+52+62. The only other ways to write 91 as a sum of distinct squares are: 91 = 12+42+52+72 and 91 = 12+32+92.
91 is the smallest pseudoprime satisfying the congruence 3n = 3 mod n.
91 is a repdigit in base 9 (111).
Read more about this topic: 91 (number)
Famous quotes containing the word mathematics:
“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)