144 (number) explained

Number:	144
Divisor:	1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144

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

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]

In other fields

• is a scale used for some scale models.
• Mahjong is usually played with a set of 144 tiles.
• The measurement, in cubits, of the wall of New Jerusalem shown by the seventh angel (Bible, Revelation 21:17). 144 also occurs in the name of Psalm 144.
• 144 is the number of square inches in a square foot.

References

• Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. London: Penguin Group. (1987): 139–140.

External links

• The Natural Number 144

Notes and References

1. Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 165
2. Cohn . J. H. E. . 10.1112/jlms/s1-39.1.537 . The Journal of the London Mathematical Society . 163867 . 537–540 . On square Fibonacci numbers . 39 . 1964.
3. 2016-05-28 .
4. Lander . L. J. . Parkin . T. R. . Counterexample to Euler's conjecture on sums of like powers . . . 72 . 6 . 1966 . 1079 . 10.1090/S0002-9904-1966-11654-3 . free . 121274228 . 0145.04903 . 0197389.