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Number Puzzle

Across
1.This number is half of 2 down and the five digits comprising the two numbers are all different.
3. The sum of the squares of two numbers whose difference is two.
4. The sum of the cubes of two numbers.
5. This perfect square is an anagram of 3 down.

Down
1. The difference of the squares of the two numbers referred to in 3 across.
2. See 1 across.
3. The digits of this number, taken in order, form an arithmetical progression.
4. The difference of the cubes of the numbers referred to in 4 across.