In Mathematics
85 is an octahedral number, a centered triangular number, a centered square number, a decagonal number, and a Smith number.
85 is the product of two prime numbers (5 and 17), and is therefore a biprime; specifically, the 24th biprime not counting perfect squares. Together with 86 and 87, it forms the second cluster of three consecutive biprimes.
85 can be expressed as a sum of two squares in two ways, 85= 92 + 22 = 72 + 62
85 is 1111 (a repunit) in base 4; which is expected, since its two factors 5 and 17 are consecutive Fermat primes, and the base 4 is one less than the smaller factor 5.
The aliquot sum of 85 is 23 within the aliquot sequence (23,1,0) 85 being the second composite number in the 23-aliquot tree.
Read more about this topic: 85 (number)
Famous quotes containing the word mathematics:
“... though mathematics may teach a man how to build a bridge, it is what the Scotch Universities call the humanities, that teach him to be civil and sweet-tempered.”
—Amelia E. Barr (1831–1919)
“It is a monstrous thing to force a child to learn Latin or Greek or mathematics on the ground that they are an indispensable gymnastic for the mental powers. It would be monstrous even if it were true.”
—George Bernard Shaw (1856–1950)