Consider the diophantine equation -
\( x^3 + y^4 = 7 \)
The solution which was given in the book had argument starting like - "Consider the residue class of \(x^3\) modulo 13"
From where does one get motivation to check the residue class of that particular modulo?
Easy ones can be seen directly like checking residue class of modulo 3 in case of squares, modulo 7 in case of cubes, but what about others?
And yes, is there any list available of frequently used residue classes of modulo x? I think that might help many students. :)