For certain positive integers 
, and 
, 
. If 
and are prime, find 
.
Source: SCVMA Math Olympiad 2010
Solution
Since and are odd, 
and 
are odd which implies that 
is even. Hence 
is even because the sum 
is even.
implies that is an even perfect fifth power less that 
.
Case 1: 
Trial and error method: looking for prime integers and such that
too low
still too low
better
too high
Maybe we should try and closer to each other like 
and 
Case 2: Time to try 
Try 
Bingo! 
and 
Answer: 
