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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.
Since each 2 × 2 subsquare sums to the magic constant, 4 × 4 pandiagonal magic squares are most-perfect magic squares. In addition, the two numbers at the opposite corners of any 3 × 3 square add up to half the magic constant. Consequently, all 4 × 4 pandiagonal magic squares that are associative must have duplicate cells.
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. In base 12, a square number can end only with square digits (like in base 12, a prime number can end ...
This is a list of articles about prime numbers.A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem, there are an infinite number of prime numbers.
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
[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.
After all 100 spaces are filled, the digits 0 to 9 are randomly assigned to rows and columns. Payouts are based on the last digit of the score of each team at the end of the first quarter, half ...
(The first 5 perfect numbers end with digits 6, 8, 6, 8, 6; but the sixth also ends in 6.) Philo of Alexandria in his first-century book "On the creation" mentions perfect numbers, claiming that the world was created in 6 days and the moon orbits in 28 days because 6 and 28 are perfect.