125

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Number

$125$ (one hundred and twenty-five) is:

$5^3$


The length of the shortest face diagonal of the smallest cuboid whose edges and the diagonals of whose faces are all integers:
The lengths of the edges are $44$, $117$, $240$
The lengths of the diagonals of the faces are $125$, $244$, $267$.


The $3$rd power of $5$ after $(1)$, $5$, $25$:
$125 = 5^3$


The $3$rd Friedman number base $10$ after $25$, $121$:
$125 = 5^{1 + 2}$


The $4$th positive integer after $50$, $65$, $85$, and first cube, which can be expressed as the sum of two square numbers in two or more different ways:
$125 = 11^2 + 2^2 = 10^2 + 5^2 = 5^3$


The $5$th cube number after $1$, $8$, $27$, $64$:
$125 = 5 \times 5 \times 5$


The $10$th integer after $7$, $13$, $19$, $35$, $38$, $41$, $57$, $65$, $70$ the decimal representation of whose square can be split into two parts which are each themselves square:
$125^2 = 15 \, 625$; $1 = 1^2$, $5625 = 75^2$


The $13$th trimorphic number after $1$, $4$, $5$, $6$, $9$, $24$, $25$, $49$, $51$, $75$, $76$, $99$:
$125^3 = 1 \, 953 \, \mathbf {125}$


The $13$th positive integer $n$ after $0$, $1$, $5$, $25$, $29$, $41$, $49$, $61$, $65$, $85$, $89$, $101$ such that the Fibonacci number $F_n$ ends in $n$


The $17$th powerful number after $1$, $4$, $8$, $9$, $16$, $25$, $27$, $32$, $36$, $49$, $64$, $72$, $81$, $100$, $108$, $121$


The $57$th (strictly) positive integer after $1$, $2$, $3$, $\ldots$, $95$, $96$, $102$, $108$, $114$, $119$, $120$ which cannot be expressed as the sum of distinct primes of the form $6 n - 1$


Also see


Sources

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