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Aside from being the smallest square triangular number other than 1, it is also the only triangular number (other than 1) whose square root is also a triangular number. 36 is also the eighth refactorable number, as it has exactly nine positive divisors, and 9 is one of them; [3] in fact, it is the smallest positive integer with at least nine ...
The Roman numerals, in particular, are directly derived from the Etruscan number symbols: 𐌠 , 𐌡 , 𐌢 , 𐌣 , and 𐌟 for 1, 5, 10, 50, and 100 (they had more symbols for larger numbers, but it is unknown which symbol represents which number). As in the basic Roman system, the Etruscans wrote the symbols that added to the desired ...
For example, the third triangular number is (3 × 2 =) 6, the seventh is (7 × 4 =) 28, the 31st is (31 × 16 =) 496, and the 127th is (127 × 64 =) 8128. 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.
Consequently, a square number is also triangular if and only if + is square, that is, there are numbers and such that =. This is an instance of the Pell equation x 2 − n y 2 = 1 {\displaystyle x^{2}-ny^{2}=1} with n = 8 {\displaystyle n=8} .
A form of unary notation called Church encoding is used to represent numbers within lambda calculus. Some email spam filters tag messages with a number of asterisks in an e-mail header such as X-Spam-Bar or X-SPAM-LEVEL. The larger the number, the more likely the email is considered spam. 10: Bijective base-10: To avoid zero: 26: Bijective base-26
Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds.
666 is a Smith number and Harshad number in base ten. [13] [14] The 27th indexed unique prime in decimal features a "666" in the middle of its sequence of digits. [15] [c] The Roman numeral for 666, DCLXVI, has exactly one occurrence of all symbols whose value is less than 1000 in decreasing order (D = 500, C = 100, L = 50, X = 10, V = 5, I = 1 ...
An upper case numeral that is not followed by a symbol is understood as a major chord. The use of Roman numerals enables the rhythm section performers to play the song in any key requested by the bandleader or lead singer. The accompaniment performers translate the Roman numerals to the specific chords that would be used in a given key.