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25 (twenty-five) is the natural number following 24 and preceding 26.

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 demonstrations of the Pythagorean theorem.

25 is a centered octagonal number and an automorphic number.

25 has an aliquot sum of 6 and is the first 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. It is also a Somer pseudoprime based on 6.

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 x_1, x_2, \dots, x_n such that

\sum_{i=1}^{n} \frac{x_i}{x_{i+1}+x_{i+2}} \frac{n}{2}

where x_{n+1}=x_1, x_{n+2}=x_2.

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 10^n * Z + (2Z + 1) where n clearly depends on the number of digits in Z and in 2Z+1.

In religion

• In Ezekiel's vision of a new temple: The number twenty-five is of cardinal importance in Ezekiel's Temple Vision (in the Bible, Ezekiel chapters 40-48).

In sports

• The size of the full roster on a major league baseball team
• The number of points needed to win a set in volleyball under rally scoring rules (except for the fifth set), so long as the losing team's score is two less than the winning team's score (i.e., if the winning team scores 25 points, the losing team can have no more than 23 points)

Twenty five is:

Historical years

25 A.D., 25 B.C., 1925, 2025, etc.

Slang names

• Pony (British slang for £25)

References

1. Evans, I.H., Brewer's Dictionary of Phrase and Fable, 14th ed., Cassell, 1990, ISBN 0304340049

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