hi everyone .
i need a little help in a direction of how to start this question...
"For what values of c does 2x + 5y = c have exactly one strictly positive integer solution?"
im not very good with applying constraints to things . ive been told that a little bit of enumeration will be needed in near the end to get the answer though.
thank you for your time!
Thm: Given any , there exists exactly one solution such that or . Proof: Given , it is either even or odd. If is even then is a solution. If is odd, then is even, so is a solution. Call this initial solution . (Note that if is odd but , no positive solution exists, not even this initial one.)
Cor: Now for any , is also a solution. To be a strictly positive solution, , so for a second solution to exist.
Thus, for a second solution to NOT exist, or , and . So, consider the function on the domain . These resulting values of are the ones for which only one positive solution exists.