Mursalin and Agnishom Draw Diagonals!

Algebra Level 5

Mursalin and Agnishom decide to play a game where they alternately draw diagonals between the vertices of a regular \(n\)-gon. In each turn, Mursalin and Agnishom has to draw a diagonal that doesn't intersect any of the diagonals that have been already formed. Mursalin goes first. The person who is unable to make a move loses. For how many possible values of \(n\), does Agnishom have a winning strategy if \(457\leq n\leq 1003\)?

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