perfect square 奧數3條，數學高手們進。

1.
If a^3= b^2 and c^3= d^2, where a, b, c, d are positive integers; and if c-a= 25, what are a,b,c and d?
2.
Show that if a, b, c and d are integers such that m= a^2+b^2 , n= c^2+d^2 , then mn can also be expressed as the sum of the square of 2 integers.
3.
Find all 4-digit numbers ABCD so that the last 4 digits in the square of this given 4-digit number is still ABCD.

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