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pattern matching - Transformation rule for arbitrary number of argument expressions


I am failing to write a Mathematica transformation rule that replaces e.g. f[a + 3, b + 3, c + 3] with f[a, b, c] + 3 for an arbitrary number of arguments. However, f[a + 3, b + 3, c + 2] should remain untouched after the transformation.




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