125 (number)

125 is the cube of 5. It can be expressed as a sum of two squares in two different ways, 125 = 10² + 5² = 11² + 2².^[1]

125 and 126 form a Ruth-Aaron pair under the second definition in which repeated prime factors are counted as often as they occur.

Like many other powers of 5, it is a Friedman number in base 10 since 125 = 5^{1 + 2}.

125 is the center of a close triplet of perfect powers, (121 = 11², 125 = 5³, 128 = 2⁷). Excluding the trivial cases of 0 and 1, the only closer such triplet is (4,8,9) and the only other equally close is (25, 27, 32).^[2]