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In mathematics, a square number or perfect square is an integer that is the square of an integer; [1] ... 20 2 = 400 21 2 = 441 22 2 = 484 23 2 = 529 24 2 = 576 25 2 ...
Since this is also a multiple of 4 for k > 0, 2 4k ±1 ≡ ±12 (mod 20). Thus, all Mersenne numbers M 4k +1 are congruent to 11 modulo 20 and end in 11, 31, 51, 71 or 91, while Mersenne numbers M 4k −1 ≡ 7 (mod 20) and end in 07, 27, 47, 67, or 87. For the perfect numbers, define P n = 2 n−1 M n be the value which is perfect if M n is prime.
In addition, each prime factor of m/b 3 has an even exponent, so m/b 3 is a perfect square, so call this a 2; then m = a 2 b 3. For example: ... 20: 85 – 87. doi:10 ...
A perfect square is an element of algebraic structure that is equal to the square of another element. Square number, a perfect square integer. Entertainment
In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number. The next perfect number is 28, since 1 + 2 + 4 + 7 + 14 = 28.
A most-perfect magic square of order n is a magic square containing the numbers 1 to n 2 with two ... [4,] 23 107 6 105 39 122 20 136 37 138 4 121 [5,] 16 ...
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() is always a perfect square. [10] As it is only a necessary condition but not a sufficient one, it can be used in checking if a given triple of numbers is not a Pythagorean triple. For example, the triples {6, 12, 18} and {1, 8, 9} each pass the test that ( c − a )( c − b )/2 is a perfect square, but neither is a Pythagorean triple.