data/problems/141.yml
---
:id: 141
:name: Investigating progressive numbers, _n_, which are also square
:url: https://projecteuler.net/problem=141
:content: "A positive integer, _n_, is divided by _d_ and the quotient and remainder
are _q_ and _r_ respectively. In addition _d_, _q_, and _r_ are consecutive positive
integer terms in a geometric sequence, but not necessarily in that order.\n\nFor
example, 58 divided by 6 has quotient 9 and remainder 4. It can also be seen that
4, 6, 9 are consecutive terms in a geometric sequence (common ratio 3/2). \nWe
will call such numbers, _n_, progressive.\n\nSome progressive numbers, such as 9
and 10404 = 102<sup>2</sup>, happen to also be perfect squares. \n The sum of all
progressive perfect squares below one hundred thousand is 124657.\n\nFind the sum
of all progressive perfect squares below one trillion (10<sup>12</sup>).\n\n"