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68 is a Perrin number. [1] It has an aliquot sum of 58 within an aliquot sequence of two composite numbers (68, 58,32,31,1,0) to the Prime in the 31-aliquot tree. It is the largest known number to be the sum of two primes in exactly two different ways: 68 = 7 + 61 = 31 + 37. [2]
The even numbers form an ideal in the ring of integers, [13] but the odd numbers do not—this is clear from the fact that the identity element for addition, zero, is an element of the even numbers only. An integer is even if it is congruent to 0 modulo this ideal, in other words if it is congruent to 0 modulo 2, and odd if it is congruent to 1 ...
3. Between two groups, may mean that the first one is a proper subgroup of the second one. > (greater-than sign) 1. Strict inequality between two numbers; means and is read as "greater than". 2. Commonly used for denoting any strict order. 3. Between two groups, may mean that the second one is a proper subgroup of the first one. ≤ 1.
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
Even numbers are always 0, 2, or 4 more than a multiple of 6, while odd numbers are always 1, 3, or 5 more than a multiple of 6. Well, one of those three possibilities for odd numbers causes an issue.
"Take" for R, abbreviation of the Latin word recipe, meaning "take". Most abbreviations can be found in the Chambers Dictionary as this is the dictionary primarily used by crossword setters. However, some abbreviations may be found in other dictionaries, such as the Collins English Dictionary and Oxford English Dictionary.
For example, the clue "A few, we hear, add up (3)" is the clue for SUM. The straight definition is "add up", meaning "totalize". The solver must guess that "we hear" indicates a homophone, and so a homophone of a synonym of "A few" ("some") is the answer. Other words relating to sound or hearing can be used to signal the presence of a homophone ...
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