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.
(In reply to
Possibly ... by Larry)
I'm not sure what you mean by the expression x^2+y, it should be x^2+5y. In that case x can be greater than y.
For example, if x=7 and y=3 then x^2+5y=64=8^2
There's also the single positive case where x=y=4
The longest chain I've found is 89, 72, 29, 24, 20 but it doesn't wrap around: 20^2+5*89 is not a perfect square.
The largest number roughly doubles to lengthen the chain, so someone with a better program should be able to find a chain of length 10 pretty quickly. It then needs to wrap around for j^2+5a
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Posted by Jer
on 2023-11-13 14:37:11 |
re: Possibly ...
