**25**= 5

^{2}, a perfect square.

**25**has a representation as a sum of two squares:

**25**= 3

^{2}+ 4

^{2}. It is the smallest square that can be written as a sum of two squares.

**25**is the hypotenuse of a primitive Pythagorean triple:

**25**

^{2}= 7

^{2}+ 24

^{2}.

**25**is the sum of the first five odd numbers:

**25**= 1 + 3 + 5 + 7 + 9.

**25**= 3 + 4 + 5 + 6 + 7.

**25**, is one of the national games of India.

Source: Phillips, R. 1994.

*Numbers: Facts, Figures and Fiction*. Cambridge University Press.
## 1 comment:

Other properties of the number 25

25 is an octahedral number since (2n-1)(2n^2-2n+3)/3 =25 with n=3,

See A001845 and http://mathworld.wolfram.com/OctahedralNumber

25 is a octagonal number since (2n-1)=25 with n=3

25 is an automorphic number since 5^2=25 is termination of one's own number, see

A003226

25 is a Friedman number since 25=5^2 uses the same digits, see

A036057

25 is a Cullen number since n*2^2=25 with n=3, see A002064 and

http://math.world.wolfram.com/CullernNumber

25 is a number trimorphic since n^3= 5,625 where the last two digits correspond to n, with n=25, see A033819 and http:mathworld.wolfram.com/Trimorphic/Number

25 is a Hilbert number since 25=4*6+1, see A016813 and http://mathworld.wolfram.com/HilbertNumber

25 is a number of Brown since 25=4!+1

As 5^2=25, if all digits (except the exponent) is added the unit is

6^2=36

If 25 is subtracted from or added the number 6, we get two prime numbers:

25-6=19 and 25+6=31

If 25 is subtracted or added the number 12, get two prime numbers:

25-12=13 and 25+12=37

The number 25 can be represented as Pythagorean triples

25^2=15^2+20^2

25^2+312^2=313^2

Also

25=13^2-12^2

If 25^2=625 and 16^2=256, repeat 25to the end and beginning of the output.

Rafael Parra Machio

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