#### knabe

##### Well-known member

Here’s what I got.

2008 is the prime number 251 multiplied by the sum its own digits. 251 × (2 5 1)

2008 is the sum of the 9th, 14th, and 17th Fibonacci Numbers (34 377 1597)

(From Jim Pemberton) 2008 = 10 310 323; and 251 is the smallest number that can be written as the sum of 3 cubes in 2 ways (1 35353and 2 33363), and 8 itself is of course the smallest nontrivial cube … so 2008 is the smallest number that is nontrivially the sum of three cubes, multiplied by a cube.

2008 can be written as the sum of 16 consecutive positive integers: 118 119 120 … 132 133

2008 = 2 (3 23) − (2 3) × 2 3

Finally, from Noel Pixley, I got this: “Take the value of the number 2008 as expressed in base 2, 5, 7, and 8 and add them together. You get …2008!” Do you, though? When I tried it, I got 11,111,011,000 31,013 5,566 3,730 = 11,111,051,309. How late at night was it, Noel?