25 (number) - in Mathematics

In Mathematics

It is a square number, being 5² = 5 × 5. It is the smallest square that is also a sum of two (non-zero) squares: 25 = 3² + 4². Hence it often appears in illustrations of the Pythagorean theorem.

25 is a centered octagonal number, a centered square number, and an automorphic number.

25 percent is equal to 1/4.

25 has an aliquot sum of 6 and number 6 is the first (or smallest) number to have an aliquot sequence that does not culminate in 0 through a prime. Twenty-five is the aliquot sum of three integers; 95, 119, and 143. Twenty-five is the second composite member of the 6-aliquot tree.

It is the smallest base 10 Friedman number as it can be expressed by its own numbers: 5².

It is also a Cullen number. 25 is the smallest pseudoprime satisfying the congruence 7n = 7 mod n.

25 is the smallest aspiring number — a composite non-sociable number whose aliquot sequence does not terminate.

According to the Shapiro inequality, 25 is the least odd integer n such that there exist such that

where .

Within base 10 one can readily test for divisibility by 25 by seeing if the last two digits of the number match 25, 50, 75 or 00.

25 and 49 are the only perfect squares in the following list:

13, 25, 37, 49, 511, 613, 715, 817, 919, 1021, 1123, 1225, 1327, 1429, etc.

The formula in this list can be described as where n clearly depends on the number of digits in Z and in 2Z+1.

In base 30, 25 is a 1-automorphic number (displayed as the numeral 'P' or 'R' dependant on the chosen digit set), and in base 10 a 2-automorphic number.