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To my knowledge, there is no probitions against metal detecting in Peru, to begin with. So why would you need permission? Unless it's an off-limits sites there, like a historic monument, or certain protected dig location, etc.... And of course private property, then permission from the owner. But for regular public land (out in the mountains, etc...) no, you don't need "permission" for places that have no specfic laws against it, in the first place.
As for "percentages", if you mean for the govt, the only time there are "percentages" type legal stuff, is if you're talking shipwreck salvor stuff, I suppose. Typically, and realistically, for small time coin and relic hunting type stuff (beach hunting, etc...), no, there is no "govt. owns all" type thing. But then again, go figure, no matter WHAT you find (a single gold coin, let's say), I suppose if you walked in to a govt. bureaucrat there (or anywhere) and said "can I keep it?", what do you think they'd say? They'd take it, say thankyou, and you'd never see it again (except at his house on his own mantle place).
Metal detecting is common in Latin America, Mexico, Carribean, etc.... and there is no problems for casual detectors. Perhaps if you found a pyramid filled with gold, then yeah, some govt. official might say they get half, or all, or whatever. But then so too would this be the case for anywhere (look at the Mel Fisher hassles, for instance here in the USA

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But if you meant private property, then the percentages split is whatever you negotiate with that particular land-owner.
Here's an example of a metal detector dealer in Peru. This is just one example, that came from a simple search under Fisher metal detector dealers. You can do the same type search for tesoro brand, minelab brand, Whites brand, etc... and probably come up with other dealers down there. Those dealers would have more answers to your questions, as they pertain to local things, since they are probably hobbyists themselves, and deal to others who hunt around there. (and notice that detectors are sold there, so .... obviously people are metal detecting there

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MEDECTOR BOLIVIA
AV. Carrion Corrales 1085 Miraflores
La Paz - Bolivia
Phone: +591 2 - 0000000
E-mail:
ventas.peru@medector.com
Productos
Hi all!
I plan to travel to Peru with a metal detector to search treasure.
Could you help me with some questions?:
- What is the procedure for obtaining permission to search in Peru?
- What percentage gets the one who found the treasure?
- What laws regulate search with a metal detector in Peru?
Thanks in advance.