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A perfect square is an element of algebraic structure that is equal to the square of another element. Square number, a perfect square ... Perfect square trinomials, ...
So, 6 is a perfect number because the proper divisors of 6 are 1, 2, and 3, and 1 + 2 + 3 = 6. [2] [4] There is a one-to-one correspondence between the Mersenne primes and the even perfect numbers, but it is unknown whether there exist odd perfect numbers. This is due to the Euclid–Euler theorem, partially proved by Euclid and completed by ...
Proof: 2 p+1 ≡ 2 (mod q), so 2 1 / 2 (p+1) is a square root of 2 mod q. By quadratic reciprocity, every prime modulus in which the number 2 has a square root is congruent to ±1 (mod 8). A Mersenne prime cannot be a Wieferich prime. Proof: We show if p = 2 m − 1 is a Mersenne prime, then the congruence 2 p−1 ≡ 1 (mod p 2) does ...
289 is a perfect square being equal to 17². It is also the 7th number to only have 3 factors because it is a square of a prime number. 289 is the sum of perfect cubes. It is the sum of 1³+2³+4³+6³. 289 is equivalent to the sum of the first 5 whole numbers to their respective powers. It is equal to 0⁰+1¹+2²+3³+4⁴.
A square whose side length is a triangular number can be partitioned into squares and half-squares whose areas add to cubes. From Gulley (2010).The n th coloured region shows n squares of dimension n by n (the rectangle is 1 evenly divided square), hence the area of the n th region is n times n × n.
(The list of known primes of this form is A002496.) The existence of infinitely many such primes would follow as a consequence of other number-theoretic conjectures such as the Bunyakovsky conjecture and Bateman–Horn conjecture. As of 2024, this problem is open. One example of near-square primes are Fermat primes.
If you’re stuck on today’s Wordle answer, we’re here to help—but beware of spoilers for Wordle 1301 ahead. Let's start with a few hints.
Notably, absent consensus, please do not add articles about individual perfect numbers themselves (such as 6). Pages in category "Perfect numbers" The following 11 pages are in this category, out of 11 total.