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It is divisible by 3 and by 8. [6] 552: it is divisible by 3 and by 8. 25: The last two digits are 00, 25, 50 or 75. 134,250: 50 is divisible by 25. 26: It is divisible by 2 and by 13. [6] 156: it is divisible by 2 and by 13. Subtracting 5 times the last digit from 2 times the rest of the number gives a multiple of 26. (Works because 52 is ...
[8]: 30 For each positive integer k, there exist at least k different Pythagorean triples with the same hypotenuse. [8]: 31 If c = p e is a prime power, there exists a primitive Pythagorean triple a 2 + b 2 = c 2 if and only if the prime p has the form 4n + 1; this triple is unique up to the exchange of a and b.
The least common multiple of the denominators of two fractions is the "lowest common denominator" (lcd), and can be used for adding, subtracting or comparing the fractions. The least common multiple of more than two integers a, b, c, . . . , usually denoted by lcm (a, b, c, . . .), is defined as the smallest positive integer that is divisible ...
n ! {\displaystyle n!} In mathematics, the factorial of a non-negative integer , denoted by , is the product of all positive integers less than or equal to . The factorial of also equals the product of with the next smaller factorial: For example, The value of 0! is 1, according to the convention for an empty product.
Goldbach's conjecture is used when studying computation complexity. [36] The connection is made through the Busy Beaver function, where BB (n) is the maximum number of steps taken by any n state Turing machine that halts. There is a 27 state Turing machine that halts if and only if Goldbach's conjecture is false.
A highly composite number is a positive integer that has more divisors than any smaller positive integer. A related concept is that of a largely composite number, a positive integer that has at least as many divisors as any smaller positive integer. The name can be somewhat misleading, as the first two highly composite numbers (1 and 2) are not ...
Coprime integers. In number theory, two integers a and b are coprime, relatively prime or mutually prime if the only positive integer that is a divisor of both of them is 1. [1] Consequently, any prime number that divides a does not divide b, and vice versa. This is equivalent to their greatest common divisor (GCD) being 1. [2]
Trailing zero. In mathematics, trailing zeros are a sequence of 0 in the decimal representation (or more generally, in any positional representation) of a number, after which no other digits follow. Trailing zeros to the right of a decimal point, as in 12.340, don't affect the value of a number and may be omitted if all that is of interest is ...