Find ten positive integers a > b > c > d > e > f > g > h > i > j such that a^2+5b, b^2+5c, c^2+5d, ..., j^2+5a are all perfect squares.
[edit: disregard this comment, I meant x^2 + 5y, but it is just incorrect]
When I test the expression x^2 + y, it appears that when y is positive and this expression is a square, x is always less than y.
So it appears that there are no solutions.
I started on a proof but was not successful.
Edited on November 13, 2023, 4:21 pm
|
|
Posted by Larry
on 2023-11-13 11:46:24 |
Possibly ...
