@Kitonum In cases where you can easily identify a unique representative of each equivalence class, it is far more efficient to use that fact and ListTools:-Classify rather than ListTools:-Categorize. In this case, sorting a composition gives a unique representative of the equivalence classes that we want:

ListTools:-Classify(sort, combinat:-composition(7,3));

But, in this case, we only need the representative; we can discard the rest of each class:

[indices(%, 'nolist')];

So, if you have a function ECUR that returns the Equivalence Class Unique Representative, then applying such to a set S can be done with ECUR~(S). Hence, we've arrived at VV's Answer.

Because of such simplifications, there've been very few times where I've actually used Categorize. When dealing with finite sets (as must be the case in a computer program), it's usually easy to come up with a unique representative of each equivalence class.

@kristavaldes Are you sure that you weren't given a value of d (the decryption exponent) earlier, perhaps as part of another assignment? Or perhaps in an earlier assignment, you generated your own random primes p and q and exponents e and d and sent the instructor your public key (n,e) (where n = p*q, but you keep p and q secret)?

@Lottie In the code of a procedure, there are several symbols that can be used to refer generically to various parts of the procedure and its invocation. The symbol procname refers to the name by which the procedure was called. Usually this is the same as the name with which it was declared, i.e., the name to the left of proc. But this is not always the case. For example, it may be called with its declared name with a subscript added. Using procname instead of the explicitly declared name will retain that subscript.

Likewise args and _passed (which mean the same thing) are the arguments with which the procedure was actually called, which may include extra arguments that don't correspond to declared parameters.

It is for these reasons that experienced Maple programmers use constructions such as 'procname(_passed)' rather than 'Q(A)'. Another reason is that the former will never need to be changed, even if you rewrite the procedure with a different name and different names for its parameters.

All numeric BVP methods that I'm aware of, including shooting, require you to use some finite value in place of infinity.

Having solved many BVPs are this sort (nanofluid related) in the past, I know that the independent variable is eta. But that may not be apparent to other readers.

You will need to supply numeric values for Nt, Nb, Pr, Le, and M for every solution attempt.

@kristavaldes I'll be happy to provide more help when you have more information. 

@kristavaldes I may be missing something here, but I don't understand how it's possible to recover m from three (or any number of) remainders of m^e without knowing the decryption exponent d. Theoretically, it should only be possible to recover m^e from its remainders.

It's not surprising that homework assignments are given by text message these days, but this is a surprising example of that.

Are you using Maple 17 or Maple 2017? Those are different versions, with the latter being later.

@vv I strongly suspected that, but I didn't test.

I'd recommend Iterator:-PartitionFixedSize, but it has a bug. Even the example on its help page, (12,5), is wrong.

I assume the e is the encrpytion exponent. It think that it's unlikely to be 3 in a secure implementation, although 3 is sometimes used because there is some efficiency benefit to using a small e. A common choice is e = 2^16+1, which is still quite small compared to the other numbers used.

I don't think that your worksheet provides enough details to answer your Question. Could you restate the Question using the language of this webpage: https://www.di-mgt.com.au/crt_rsa.html

@Lottie Just because you're "not familiar with" with a concept, does that mean that you shouldn't use it? Isn't there some room for learning a new concept? The procname could be replaced by Q itself, and the _passed could be replaced by args or A, but the quotation marks can't be replaced. I think that the quotation marks are what scare you. I'll admit that the quotation marks are a difficult thing to learn, but this particular usage of them---to make a procedure return unevaluated when it's passed nonnumeric arguments---is very standard. 

@Lottie The purpose of procedure Q is to defer the evaluation of the expression Q(A) (which is needed in the animate command) until numeric (realcons) values are supplied for A. Those values will be supplied by animate due to its argument A= 2..3. When a numeric value is given, it'll be used to set the parameter A that occurs in the ODE system. Note that there are actually three different variables named A in use here, used a total of seven times:

1. The A in the ODE system and the parameters argument to dsolve;
2. The three occurences of A in procedure Q;
3. The two occurence of A in the animate command.

It's not necessary that the same symbol 'A' be used for these three. But that's a natural way to code it. They do all represent exactly the same thing, but Maple considers them different.

@adel-00 For a parametric plot, the third member of the list that is the first argument of plot must be of the form name=range(realcons). So, you can't have sqrt(Y)= 0..1; you must change it to something like Y= 0..1.

@Carl Love My answer above applies to the general case of an equation in three variables. Since it can be solved for one of the variables, epsilon, as shown by Kitonum below, this is the better way for this case. It's almost always better to solve for a variable than to use implicitplot3d.

@adel-00 The problem is that the contourplot command is not prepared to handle an implicit expression. But implicitplot3d can plot contours, and if these are viewed correctly, they'll look like a 2D contourplot.. So, repeat the same implitcitplot3d, and add the options grid= [49$3], style= contour, orientation= [-90,0]. The orientation makes it look like a 2D plot, but if you pick it up and rotate it, you'll see that it's not.

@adel-00 Please give the expressions that set the  numeric values of the lambdas. I know  that you had those in your separate Question, but that's deleted now.