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A cube number, or a perfect cube ... 20 3 = 8000 30 3 = 27,000 40 3 = 64,000 50 3 = ... For example, the sum of the first 5 cubes is the square of the 5th triangular ...
Nicomachus, at the end of Chapter 20 of his Introduction to Arithmetic, pointed out that if one writes a list of the odd numbers, the first is the cube of 1, the sum of the next two is the cube of 2, the sum of the next three is the cube of 3, and so on.
The first in decimal: 4, 6, 8, 9, 12, 18, 20, 22, 24, 26, 28, 30 (sequence A046760 in the OEIS). An economical number has been defined as a frugal number, but also as a number that is either frugal or equidigital.
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.
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.
Korselt was the first who observed the basic properties of Carmichael numbers, but he did not give any examples. That 561 is a Carmichael number can be seen with Korselt's criterion. Indeed, 561 = 3 ⋅ 11 ⋅ 17 {\displaystyle 561=3\cdot 11\cdot 17} is square-free and 2 ∣ 560 {\displaystyle 2\mid 560} , 10 ∣ 560 {\displaystyle 10 ...
The popularity of the Cube is reflected in its strong sales—in 2022, 5.75 million units of the official Rubik’s Cube were sold globally and that figure was up 14% year-to-date, according to ...
The sum of four cubes problem [1] asks whether every integer is the sum of four cubes of integers. It is conjectured the answer is affirmative, but this conjecture has been neither proven nor disproven. [2] Some of the cubes may be negative numbers, in contrast to Waring's problem on sums of cubes, where they are required to be positive.