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The final digit of a triangular number is 0, 1, 3, 5, 6, or 8, and thus such numbers never end in 2, 4, 7, or 9. A final 3 must be preceded by a 0 or 5; a final 8 must be preceded by a 2 or 7. In base 10, the digital root of a nonzero triangular number is always 1, 3, 6, or 9. Hence, every triangular number is either divisible by three or has a ...
With even cubes, there is considerable restriction, for only 00, o 2, e 4, o 6 and e 8 can be the last two digits of a perfect cube (where o stands for any odd digit and e for any even digit). Some cube numbers are also square numbers; for example, 64 is a square number (8 × 8) and a cube number (4 × 4 × 4).
Visual proof that 3 3 + 4 3 + 5 3 = 6 3. 216 is the cube of 6, and the sum of three cubes: = = + +. It is the smallest cube that can be represented as a sum of three positive cubes, [1] making it the first nontrivial example for Euler's sum of powers conjecture.
A cube has all multiplicities divisible by 3 ... A factorial x! is the product of all numbers from 1 to x. The first: 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, ...
Distances between vertices of a double unit cube are square roots of the first six natural numbers due to the Pythagorean theorem (√7 is not possible due to Legendre's three-square theorem) The first numbers that cannot be expressed as the sum of three squares (i.e. numbers that can be expressed as n = 4 a ( 8 b + 7 ) {\displaystyle n=4^{a ...
It is also the product of the first four composite numbers (4, 6, 8, ... Where 1728 is the cube of 12, the sum 1 + 728 = 729 = 9 3. The digit sum of 1728 is 18.
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
In geometry, a 6-cube is a six-dimensional hypercube with 64 vertices, 192 edges, 240 square faces, 160 cubic cells, 60 tesseract 4-faces, and 12 5-cube 5-faces. It has Schläfli symbol {4,3 4}, being composed of 3 5-cubes around each 4-face. It can be called a hexeract, a portmanteau of tesseract (the 4-cube) with hex for six (dimensions) in ...