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  2. Squared triangular number - Wikipedia

    en.wikipedia.org/wiki/Squared_triangular_number

    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 nth coloured region shows n squares of dimension n by n (the rectangle is 1 evenly divided square), hence the area of the nth region is n times n x n.

  3. List of prime numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_prime_numbers

    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. Subsets of the prime numbers may be generated with various formulas for primes.

  4. Triangular number - Wikipedia

    en.wikipedia.org/wiki/Triangular_number

    A square whose side length is a triangular number can be partitioned into squares and half-squares whose areas add to cubes. This shows that the square of the n th triangular number is equal to the sum of the first n cube numbers. Also, the square of the n th triangular number is the same as the sum of the cubes of the integers 1 to n.

  5. List of Mersenne primes and perfect numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_Mersenne_primes...

    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.

  6. Centered cube number - Wikipedia

    en.wikipedia.org/wiki/Centered_cube_number

    Because of the factorization (2n + 1)(n 2 + n + 1), it is impossible for a centered cube number to be a prime number. [3] The only centered cube numbers which are also the square numbers are 1 and 9, [4] [5] which can be shown by solving x 2 = y 3 + 3y, the only integer solutions being (x,y) from {(0,0), (1,2), (3,6), (12,42)}, By substituting a=(x-1)/2 and b=y/2, we obtain x^2=2y^3+3y^2+3y+1.

  7. Fla. Man Accused of Beating Golfer to Death With Golf Clubs ...

    www.aol.com/fla-man-accused-beating-golfer...

    A Florida man is accused of beating another man to death with golf clubs on a course in Palm Beach County. A probable cause affidavit filed by the Palm Beach Gardens Police Department obtained by ...

  8. James R. Houghton - Pay Pals - The Huffington Post

    data.huffingtonpost.com/paypals/james-r-houghton

    From January 2008 to May 2009, if you bought shares in companies when James R. Houghton joined the board, and sold them when he left, you would have a -24.9 percent return on your investment, compared to a -39.2 percent return from the S&P 500.

  9. Table of prime factors - Wikipedia

    en.wikipedia.org/wiki/Table_of_prime_factors

    An economical number has been defined as a frugal number, but also as a number that is either frugal or equidigital. gcd( m , n ) ( greatest common divisor of m and n ) is the product of all prime factors which are both in m and n (with the smallest multiplicity for m and n ).

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