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 _    _     _____      _____     ___      _  __  
| \  / ||  |  ___||   / ___//   / _ \\   | |/ // 
|  \/  ||  | ||__     \___ \\  / //\ \\  | ' //  
| .  . ||  | ||__     /    // |  ___  || | . \\  
|_|\/|_||  |_____||  /____//  |_||  |_|| |_|\_\\ 
`-`  `-`   `-----`  `-----`   `-`   `-`  `-` --`

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Text this: On a class of equations induced by a nilpotent operator and its applications