144 (number)

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]

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.

• 1:144 scale 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.

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

Wikimedia Commons has media related to 144 (number).

• The Natural Number 144