144 (number)
| ||||
|---|---|---|---|---|
| Cardinal | one hundred forty-four | |||
| Ordinal | 144th (one hundred forty-fourth) | |||
| Factorization | 24 × 32 | |||
| Divisors | 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 | |||
| Greek numeral | ΡΜΔ´ | |||
| Roman numeral | CXLIV, cxliv | |||
| Binary | 100100002 | |||
| Ternary | 121003 | |||
| Senary | 4006 | |||
| Octal | 2208 | |||
| Duodecimal | 10012 | |||
| Hexadecimal | 9016 | |||
144 (one hundred [and] forty-four) is the natural number following 143 and preceding 145. It is coincidentally both the square of twelve (a dozen dozens, or one gross.) and the twelfth Fibonacci number, and the only nontrivial number in the sequence that is square.[1][2]
Mathematics
[edit]144 is a highly totient number.[3]
144 is the smallest number whose fifth power is a sum of four (smaller) fifth powers. This solution was found in 1966 by L. J. Lander and T. R. Parkin, and disproved Euler's sum of powers conjecture. It was famously published in a paper by both authors, whose body consisted of only two sentences:[4]
A direct search on the CDC 6600 yielded
275 + 845 + 105 + 1335 = 1445
as the smallest instance in which four fifth powers sum to a fifth power. This is a counterexample to a conjecture by Euler that at least n nth powers are required to sum to an nth power, n > 2.
In other fields
[edit]
- 1:144 scale is a scale used for some scale models.
References
[edit]- ^ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 165
- ^ Cohn, J. H. E. (1964). "On square Fibonacci numbers". The Journal of the London Mathematical Society. 39: 537–540. doi:10.1112/jlms/s1-39.1.537. MR 0163867.
- ^ Sloane, N. J. A. (ed.). "Sequence A097942 (Highly totient numbers: each number k on this list has more solutions to the equation phi(x) equal to k than any preceding k.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
- ^ Lander, L. J.; Parkin, T. R. (1966). "Counterexample to Euler's conjecture on sums of like powers". Bull. Amer. Math. Soc. 72 (6). American Mathematical Society: 1079. doi:10.1090/S0002-9904-1966-11654-3. MR 0197389. S2CID 121274228. Zbl 0145.04903.
- Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. London: Penguin Group. (1987): 139–140.
External links
[edit]
