In Mathematics
Forty is an octagonal number, and as the sum of the first four pentagonal numbers, it is a pentagonal pyramidal number. Adding up some subsets of its divisors (e.g., 1, 4, 5, 10 and 20) gives 40, hence 40 is a semiperfect number.
Given 40, the Mertens function returns 0. 40 is the smallest number n with exactly 9 solutions to the equation φ(x) = n.
Forty is the number of n-queens problem solutions for n = 7.
Since 402 + 1 = 1601 is prime, 40 is a Størmer number.
40 is a repdigit in base 3 (1111) and a Harshad number in base 10.
Read more about this topic: 40 (number)
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“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)
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