# Number Gossip

(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)

## Unique Properties of 144

• 144 is a dozen dozens, or one gross
• 144 is the only composite square in the Fibonacci sequence
• 144 is the smallest square such that there exists another square - 441 - with the same set of digits
• 144 is the smallest abundant Fibonacci number
• 144 is the largest sum-product integer - the integer that is equal to the sum of its digits times the product of its digits
• 144 is the smallest square perimeter of a primitive Pythagorean triangle
• 144 is the smallest square with internal digits also forming a non-zero square
• 144 is the smallest number such that its fifth power is the sum of fewer than five other fifth powers, thus disproving Euler's sum of powers conjecture
• 144 is the smallest three-digit number in which the sum of distinct digits of the number equals the sum of its distinct prime divisors (144 = 24*34 and 1 + 4 = 2 + 3); [Cramer] checked* 79 is the least positive integer requiring the maximum number of terms, namely 19, to be expressed as a sum of positive fourth powers