## Thursday, August 5, 2010

### 819

819 = 32 x 7 x 13.

819 is 1100110011 in base 2 (binary) and 333 in base 16.

819 is the largest three-digit number whose square (670761) and cube (549353259) use different digits.

819 is the smallest number such that it and its successor (820) are both the product of two primes and the square of a prime: 820 = 22 x 5 x 41.

In 1944, RenÃ© BarthÃ©lemy developed an 819-line television standard.

#### 1 comment:

Anonymous said...

Other properties of the number 819
The number 819 can be represented as:
819=11^2+13^2+23^2=13^2+17^2+19^2
819=2^3+5^3+7^3+7^3=3^3+4^3+6^3+8^3
819=3^6+90
819 divides 64^2-1
819 is the sum of consecutive prime numbers from 13-79:
819=Sum[P,P,13,79]=13+17+19+23+...+71+73+79
819 is the sum of the squares between 1^2 and 13^2:
819=Sum[n^2,1,13]=1^2+2^2+3^2 +...+ 11^2+12^2+13^2,see A000330
819=n(n+1)(2n+1)/6 with n=13 is the square pyramidal number indicated
As a difference of two squares:
819=50^2-41^262^2-55^2
As opposed to a square and another number with different exponents:
819 = 30 ^ 2-3 ^ 4 = 38 ^ 2-5 ^ 4
As Pythagorean triples:
819^2=315^2+756^2
819^2+1900^2=2069^2
819^2+6820^2=6869^2
819^2+4100^2=4181^2
It can also be represented as the sum of a square and a cousin
819=10^2+719=20^2+419=16^2+563
Rafael Parra Machio