Mate in 4

The incredible key is 1.Rb5!.

To prevent Rb8#, Black has no choice but to take the rook, but both captures open up crucial lines for White:

1…axb5 2.Nf6! threat: 3.Rc8# — a sparkling decoy.

2…Rxf6 3.Qa1 threat: 4.Qa8#

3…Na4 4.Qxf6#

The second variation is analogous:

1…cxb5 2.Nf8! threat: 3.Rc8#

2…Rxf8 3.Qf3 threat: 4.Qa8#

3…Nd5 4.Qxf8#

A spotless gem of a problem.