144 | |||||||||
---|---|---|---|---|---|---|---|---|---|
Numbers 100 - 199 | |||||||||
100 | 101 | 102 | 103 | 104 | 105 | 106 | 107 | 108 | 109 |
110 | 111 | 112 | 113 | 114 | 115 | 116 | 117 | 118 | 119 |
120 | 121 | 122 | 123 | 124 | 125 | 126 | 127 | 128 | 129 |
130 | 131 | 132 | 133 | 134 | 135 | 136 | 137 | 138 | 139 |
140 | 141 | 142 | 143 | 144 | 145 | 146 | 147 | 148 | 149 |
150 | 151 | 152 | 153 | 154 | 155 | 156 | 157 | 158 | 159 |
160 | 161 | 162 | 163 | 164 | 165 | 166 | 167 | 168 | 169 |
170 | 171 | 172 | 173 | 174 | 175 | 176 | 177 | 178 | 179 |
180 | 181 | 182 | 183 | 184 | 185 | 186 | 187 | 188 | 189 |
190 | 191 | 192 | 193 | 194 | 195 | 196 | 197 | 198 | 199 |
A gross or great dozen is equal to 144 = 122, or one dozen dozen. [1] It is a commonly used quantity by small wholesalers.
In Czech language, 144 is called "veletucet", which means "great-twelve".
Aarex Tiaokhiao calls this number duodecimal-booiol.[2]
Furthermore, it is the largest possible number of shopping hours in most weeks in some countries, since they have laws requiring observation of a weekly rest day.
Properties[]
- It is a composite number.
- 144 is the smallest known integer n such that \(n^5\) can be expressed as 4 5th powers; \(27^5 + 84^5 + 110^5 + 133^5 = 144^5\). It is the first counterexample of Euler's sum of powers conjecture found with CDC 6600 computer by Lander and Parkin in 1966.[3]
- It is the largest Fibonacci number that is also a square. Indeed, it's the largest Fibonacci number to be any perfect power.[4]Theorem 1
- It is the smallest positive integer n for which the number nn cannot be represented in the double-precision floating-point format.
- 5144 is the first power of 5 larger than a googol.
In chess[]
It is also the number of possible king moves in 5×5 minichess.
In radiocommunications[]
The 2-meter band starts at 144 MHz.
See also[]
Sources[]
- ↑ Gross
- ↑ Part 1 (LAN) - Aarex Googology
- ↑ L. J. Lander & T. R. Parkin. "Counterexample to Euler’s conjecture on sums of like powers". Bulletin of the America Mathematical Society, 1966; 72, 1079. doi:10.1090/S0002-9904-1966-11654-3
- ↑ Florian Luca, Yann Bugeaud, Maurice Mignotte, Samir Siksek, Fibonacci numbers at most one away from a perfect power. Elem. Math. 63 (2008), no. 2, pp. 65–75. doi:10.4171/EM/89