What is the meaning of _c1 ?

Thats Mathcad's way to say the any integer is a solution of the equation.

Here you see what it looks like when Mathcad tells us that every even / every odd integer is solution

and don't ask why Mathcad now had chosen _n instead of _c1.

But Mathcad is pretty lame in that kind of "fully" solutions and will only work OK for very basic equations.

Look at this:

Is this Mathcad's way to say "every real number is solution (which would be correct)? Possibly yes, but its obviously not able to simplify the answer to say "any real".

Lets help Mathcad a little bit and lets assume m is real:

Now it got even worse. Did I already mention that assume ever so often does not work as expected? We can let Mathcad simplify which makes the result a bit better but still not desireable.

Now lets tell Mathcad we are only interested in positive solutions (which automatically assumes real, of course).

Now thats really bad! The solution is correct but its not positive, as demanded, and sure not what we would expect when we chose "fully".

Lets help Mathcad even further and lets demand that m should be an integer:

Great! If we know the solution and tell Mathcad what it is at least Mathcad will confirm its true.

So what you learn fron this is that you should use a tool for what it was made for. And Mathcad sure was not made for integer arithmetic, number theory or the like.