natural numbers?

Question

If m , n belongs to W, what are the least values of m and n respectively for

m[(0.2)^(2.5n)] belongs to N

Question :
what is W ?
whats the function m[//blah] .....is it closed function or what it is called ?

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m[(0.2)^(2.5n)] = m[5^(-5n/2)]

How ?

Answer 1

W is not a standard notation for any set I know, so you'll have to answer that yourself.
m[...] is not a function; it merely means that m is multiplied by (0.2)^(2.5n).

If W = Z+ (the set of positive integers), for example - I think this is the most likely case - then note that
m[(0.2)^(2.5n)] = m[5^(-5n/2)]
We will need n to be even to get a whole power of 5, so the smallest possible n would be n = 2. Then we have m.5^(-5) so the smallest possible value of m to make the result an integer would be m = 5^5 = 3125 (so the result is 1).

If W is a different set, the smallest values for m and n will differ.

Answer 2

i never heard of W. It must be defined in the place you found it, somewhere. Also never heard of [ ], function, maybe its a simple bracket. Well I know about [ ] which is the integer part of a number, but this doesnt make sense in this context.

Also you want to say "respectively for which.... ". Its more correct.