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It is a win for white, though might take a while. Black can throw in a ton of annoying checks. The general idea is that you work your way towards the black rook until he can't check you, than move the pawn up. Rinse and repeat until the rook is forced to sac himself for the pawn. Note that basically ever case is unique and there are exceptions.
It's a draw after Rf5+ (the only move that draws!), by giving a ton of checks. Black draws with a king on a1, a2, a3, d4, d5, d6, d7, d8, g7 or h7 only.
Thanks to the tablebases :P
With the "a" pawn (or h one) you can draw with the black king near by, in the c or d column. Here you have the black king very far from the pawn, so with exact play white should win. I think this is the main idea as far as I know, not sure if this concrete position has some trick to draw, you tell us
That is a clear draw. That is the Vančura Position. White has no way to win that. There is a good video on this technique in the Videos section.
This is a draw for black, after playing Rf4+. Black can keep checking the white king. If white king comes closer, Black rook shifts between b6 and g6.
Once white pushes pawn to a7, black rook goes behind the pawn to a6, and stays on a file, until white king comes to b file, when check either pushes him away, or back to a file.
(edit) I guess riuryK beat me this time...
It is important not to move king to f file, or to 6th rank.If king is on f file, that allows white to push the pawn to 7thrank, and then allow white to take it, by playing Rh8, as in this study: http://www.chess.com/forum/category/endgames/a-rook-and-pawn-endgame
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