Tuesday, July 27, 2010

975

975 = 3 x 52 x 13.

975 is 1111001111 in base 2 (binary).

975 is 33033 in base 4, 4303 in base 6, 1303 in base 9, and 303 in base 18.

975 is a number that cannot be written as a sum of three squares.

975 is the number of 11-ominoes that contain one hole. The Wright R-975 Whirlwind was a radial engine developed in the United States by Wright Aeronautical.

1 comment: Anonymous said...

Other properties of the number 975
The number 975 can be represented as:
975=2^10-7^2
975=6^2+11^2+17^2+23^2=9^2+11^2+17^2+22^2
975=11^2+13^2+18^2+19^2
975 divides 49^6-1
As hypotenuse of the Pythagorean triples following:
975^2=108^2+969^2=240^2+945^2
975^2=273^2+936^2=375^2+900^2
975^2=495^2+840^2=585^2+780^2
975^2=612^2+759^2
As a leg of the following Pythagorean triples:
975^2+448^2=1073^2
975^2+2000^2=2225^2
975^2+2728^2=2897^2
975^2+52808^2=52817^2
975^2+475312^2=47313^2
975=Q(n)=Q(n+1) where Q is the Euler function of n=975 as
975=Q(975) = Q(975+1)=480, see A001274 and http://mathwoorld.wolfram.com/TotientFunction
The number 975 has finite representations as the sum of a square but the product of an integer plus the square of 5:
975=5^2+38*5^2=10^2+35*5^2=15^2+30*5^2
975=20^2+23*5^2=25^2+14*5^2=30^2+3*5^2
and also as opposed to a square and entirely a product of a square of 5 with infinite representations:
975=35^2-10*5^2=45^2-42*5^2
975=50^2-61*5^2=55^2-82*5^2
975=60^2-105*5^2=65^2-130*5^2
Rafael Parra Machio