Having tried my hand at sudoku, the thought occurred to me, I wonder if it is possible to make a sudoku with the additional feature that each digit occurs only once on a diagonal.

With the help of a small computer program I found that it is not possible with all 9 digits. It is however possible to make a sudoku in which for 7 of the 9 digits each occurrence of that digit occurs only once on the 2 diagonals on which it occurs.

There is only 1 unique sudoku with this feature.

So, here is a puzzle in which for 7 of the digits, each occurrence of that digit is also the only occurrence of that digit on the 2 diagonals it occurs.

.5. ..1 .2.

9.. ..3 6..

.76 2.. .53

5.. 1.. .67

... 3.7 ...

38. ..5 ..1

71. .2. 83.

..8 7.. ..9

.4. 5.. .1.

Addenum

After posting this it was discovered by udosuk that the additional feature applies to the 7 digits only. The 2 remaining digits have two ways that they can be placed in the grid. see udosuk below. (after you have solved the puzzle)