What is the difference between motivation and intuition of a theorem/result? Are they same or different in some way?
Edit 1
To me intuition appears as the set of ideas (which may or may not contain part of the formal proof?) which validates our result (partially or fully?) and motivation as the set of ideas that induces/inspires the birth of a different result.
So, suppose we didn't knew about Fermat's Little Theorem, and then we see the pattern- $2|(a^2-a)$, $3|(a^3-a)$, $5|(a^5-a)$- each one of which having it's own separate proof established through algebra, so does this(& similarly other ones which are mathematically similar to these and whose divisor is a prime) set of results act as a motivation(induces/inspires) or intuition(partially validates/verifies on a case by basis) for Fermat's Little Theorem?