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Add the last digit to twice the rest. The result must be divisible by 8. 56: (5 × 2) + 6 = 16. The last three digits are divisible by 8. [2] [3] 34,152: examine divisibility of just 152: 19 × 8. The sum of the ones digit, double the tens digit, and four times the hundreds digit is divisible by 8. 34,152: 4 × 1 + 5 × 2 + 2 = 16. 9
2025 = 45 2, square of the sum of the first nine positive integers (and therefore sum of the cubes of the first nine positive integers, by Nicomachus's theorem), centered octagonal number, [19] lowest number with exactly 15 odd divisors. [20] Current calendar year. Sum from 11 to 64. Sum of odd numbers from 1 to 89.
d() is the number of positive divisors of n, including 1 and n itself; σ() is the sum of the positive divisors of n, including 1 and n itselfs() is the sum of the proper divisors of n, including 1 but not n itself; that is, s(n) = σ(n) − n
It is a semiperfect number, [2] equal to the concatenation of two of its proper divisors (24 and 40). [ 3 ] It is also the 12th highly composite number , [ 4 ] with 20 divisors in total, more than any smaller number; [ 5 ] and a refactorable number or tau number, since one of its divisors is 20, which divides 240 evenly.
20412 = Leyland number: [5] 9 3 + 3 9; 20540 = square pyramidal number [6] 20569 = tetranacci number [7] 20593 = unique prime in base 12; 20597 = k such that the sum of the squares of the first k primes is divisible by k. [8] 20736 = 144 2 = 12 4, 10000 12, palindromic in base 15 (6226 15), also called a dozen great-gross in some duodecimal ...
1802 = 2 × 30 2 + 2 = number of points on surface of tetrahedron with edge length 30, [141] number of partitions of 30 such that the number of odd parts is a part [173] 1803 = number of decahexes that tile the plane isohedrally but not by translation or by 180-degree rotation (Conway criterion) [ 423 ]
30 000 600 003 A common, trivial extension of the aforementioned example is to arrange the digits 0 to 9 to make a 10 digit number in the same way, the result is 3816547290. This is a pandigital polydivisible number.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.