Precisely I cannot explain it...because using software is not same coding 
software ..people , not me, are coding SAGE (and other modules included 
into  it)

Usually : assume()  is Python call for "assuming something", and if not 
true..then software stops

But here, it's a constraint...it's a parameter for next  Python functions 
(here solve)...and the solve() function will get rid of not integer roots.

I assume this behavior, but I am not sure,..again..because I had never 
written SAGE code.

I don't know really why you need to solve "induction problem"..but if you 
really want to do (and have no other ideas about how to do that using 
different maths ways)...then search again on Internet, browse forum python 
(not necessarily SAGE) and maybe you will see the light in your dark quest.

Dominiqe.

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