Number Theory
If is the divisor function and is the Euler-Mascheroni constant, then 5040 is the largest known number for which this inequality holds:
- .
This is somewhat unusual, since in the limit we have:
Guy Robin showed in 1984 that the inequality fails for all larger numbers if and only if the Riemann hypothesis is true.
Read more about this topic: 5040 (number)
Famous quotes containing the words number and/or theory:
“At thirty years a woman asks her lover to give her back the esteem she has forfeited for his sake; she lives only for him, her thoughts are full of his future, he must have a great career, she bids him make it glorious; she can obey, entreat, command, humble herself, or rise in pride; times without number she brings comfort when a young girl can only make moan.”
—Honoré De Balzac (1799–1850)
“Don’t confuse hypothesis and theory. The former is a possible explanation; the latter, the correct one. The establishment of theory is the very purpose of science.”
—Martin H. Fischer (1879–1962)