## Friday, August 13, 2010

### 845

845 = 5 x 132.

845 is 1101001101 in base 2 (binary) and 31031 in base 4; it is 1515 in base 8 and 500 in base 13.

845 has three representations as a sum of two squares: 845 = 22 + 292 = 132 + 262 = 192 + 222.

845 is the hypotenuse of two primitive Pythagorean triples: 8452 = 1162 + 8372 = 1232 + 8362.

845 is a number n for which 8n + 1 and 8n + 3 are twin primes: 8 x 845 + 1 = 6761 and 8 x 845 + 3 = 6763.

845 Naema is an asteroid discovered in 1916.

#### 1 comment:

Anonymous said...

Other characters of the number 845
845 can be represented as
845=10^2+13^2+24^2=11^2+18^2+20^2
845=2^10-179=2^4+829^=2^6+521
845 can be represented as Pythagorean triples
845^2=325^2+780^2=429^2+728^2
845^2=507^2+676^2=595^2+600^2
Further partners
845=6^2+809=12^2+701=24^2+269=28^2 +61
The two cousins that make up the product of 845 are of the form 4k +1, then
845 number can be represented as
5=(2+i)(2-i)=2^2+1^2=(2+i)(1+2i)(-i)
13=(3+2i)(3-2i)=3^2+2^2=(3+2i)(2+3i)(-i), then
845=(2+i)(1+2i)[(3+2i)(2+3i)]^2 (i)=5*13^2
Rafael Parra Machio