Do you mean separate solutions to each of those equations or solutions that satisfy all the equations simultaneously?

Is b considered fixed and a1 and a2 the variables to solve for?  

@vv wrote:

• As I understand, you have to find m,e  knowing N = m^e.
  That's not very complicated. Using ifactor(N, squfof)   it will be easy to guess/find them.

If it's possible the find m knowing N = m^e, then what's the point of using RSA?

@vazzz No result yet. It's used about 4 hours of CPU time so far. The computer went to sleep due to lack of keyboard activity, but I just resumed it.

@kristavaldes Your worksheet does correctly recover the value of X = m^e from its three remainders. But I don't see how that can be used to get simply m even if you knew e.

@AliGH I can't test if you don't post your code.

@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.