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A perfect parallelepiped is a parallelepiped with integer-length edges, face diagonals, and body diagonals, but not necessarily with all right angles; a perfect cuboid is a special case of a perfect parallelepiped. In 2009, dozens of perfect parallelepipeds were shown to exist, [18] answering an open question of Richard Guy. Some of these ...
Every odd perfect square is a centered octagonal number. The difference between any two odd perfect squares is a multiple of 8. The difference between 1 and any higher odd perfect square always is eight times a triangular number, while the difference between 9 and any higher odd perfect square is eight times a triangular number minus eight.
1729 can be expressed as a sum of two positive cubes in two ways, illustrated geometrically. 1729 is also known as Ramanujan number or Hardy–Ramanujan number , named after an anecdote of the British mathematician G. H. Hardy when he visited Indian mathematician Srinivasa Ramanujan in hospital.
When a triple of numbers a, b and c forms a primitive Pythagorean triple, then (c minus the even leg) and one-half of (c minus the odd leg) are both perfect squares; however this is not a sufficient condition, as the numbers {1, 8, 9} pass the perfect squares test but are not a Pythagorean triple since 1 2 + 8 2 ≠ 9 2. At most one of a, b, c ...
In mathematics, Hall's conjecture is an open question on the differences between perfect squares and perfect cubes.It asserts that a perfect square y 2 and a perfect cube x 3 that are not equal must lie a substantial distance apart.
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 1939, B. Rosser and R. J. Walker published a series of papers on diabolic (perfect) magic squares and cubes. They specifically mentioned that these cubes contained 13m 2 correctly summing lines. They also had 3m pandiagonal magic squares parallel to the faces of the cube, and 6m pandiagonal magic squares parallel to the space-diagonal planes ...
Attila Pethő proved in 2001 that there is only a finite number of perfect power Fibonacci numbers. [50] In 2006, Y. Bugeaud, M. Mignotte, and S. Siksek proved that 8 and 144 are the only such non-trivial perfect powers. [51] 1, 3, 21, and 55 are the only triangular Fibonacci numbers, which was conjectured by Vern Hoggatt and proved by Luo Ming ...