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if the last digit of a number is 2 or 8, its square ends in an even digit followed by a 4; if the last digit of a number is 3 or 7, its square ends in an even digit followed by a 9; if the last digit of a number is 4 or 6, its square ends in an odd digit followed by a 6; and; if the last digit of a number is 5, its square ends in 25.
Every even perfect number ends in 6 or 28, base ten; and, with the only exception of 6, ends in 1 in base 9. [55] [56] Therefore, in particular the digital root of every even perfect number other than 6 is 1. The only square-free perfect number is 6. [57]
In their book, Kathleen Ollerenshaw and David S. Brée give a method of construction and enumeration of all most-perfect magic squares. They also show that there is a one-to-one correspondence between reversible squares and most-perfect magic squares. For n = 36, there are about 2.7 × 10 44 essentially different most-perfect magic squares.
[7] [8] [9] It is widely believed, [10] but not proven, that no odd perfect numbers exist; numerous restrictive conditions have been proven, [10] including a lower bound of 10 1500. [11] The following is a list of all 52 currently known (as of January 2025) Mersenne primes and corresponding perfect numbers, along with their exponents p.
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
The stock market will have a strong year. The Russell 2000 small-cap index underperformed the S&P 500 by 15 percentage points. This came close to happening at one point, with the average 30-year ...
9 is the sum of the cubes of the first two non-zero positive integers + which makes it the first cube-sum number greater than one. [5] A number that is 4 or 5 modulo 9 cannot be represented as the sum of three cubes .
We are also increasing our adjusted EPS outlook by $0.15 on the low end and $0.13 on the high end, putting the new range at $5.50 to $5.58, up from $5.35 to $5.45, improved segment profit outlook ...