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38 is the sum of the squares of the first three primes. 37 and 38 are the first pair of consecutive positive integers not divisible by any of their digits. 38 is the largest even number which cannot be written as the sum of two odd composite numbers. The sum of each row of the only non-trivial (order 3) magic hexagon is 38. [4]
The power of 3 multiplying a is independent of the value of a; it depends only on the behavior of b. This allows one to predict that certain forms of numbers will always lead to a smaller number after a certain number of iterations: for example, 4a + 1 becomes 3a + 1 after two applications of f and 16a + 3 becomes 9a + 2 after four applications ...
For example, −4, 0, and 82 are even numbers, while −3, 5, 7, and 21 are odd numbers. The above definition of parity applies only to integer numbers, hence it cannot be applied to numbers like 1/2 or 4.201.
Farey sequences are very useful to find rational approximations of irrational numbers. [15] For example, the construction by Eliahou [16] of a lower bound on the length of non-trivial cycles in the 3x+1 process uses Farey sequences to calculate a continued fraction expansion of the number log 2 (3).
A compound fraction is a fraction of a fraction, or any number of fractions connected with the word of, [22] [23] corresponding to multiplication of fractions. To reduce a compound fraction to a simple fraction, just carry out the multiplication (see § Multiplication ).
It examines problems like how prime numbers are distributed and the claim that every even number is a sum of two prime numbers. [83] Algebraic number theory employs algebraic structures to analyze the properties of and relations between numbers. Examples are the use of fields and rings, as in algebraic number fields like the ring of integers ...
If n is not a natural number, the product may still make sense; for example, multiplication by −1 yields the additive inverse of a number. A circular slide rule. In the real and complex numbers, addition and multiplication can be interchanged by the exponential function: [80] + =.
If the divisor has a fractional part, one can restate the problem by moving the decimal to the right in both numbers until the divisor has no fraction, which can make the problem easier to solve (e.g., 10/2.5 = 100/25 = 4). Division can be calculated with an abacus. [14]
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