回複：四位平方數，前兩位和後兩位都相同，怎麽求？（知道是7744，但怎麽推呢？

Let your 4 digit number be aabb=x^2, where a and b are single digit numbers.
Then 11(100a+b)=x^2. Since 11 is a prime, 11 divides x, hence 11 divides (100a+b).
Consequently, 11 divides a+b (since 100a=99a+a). But 0 Therefore we have
9a+(a+b)/11=(x/11)^2,
or 9a+1=y^2, where we write y=x/11.
Finally since 9a=(y+1)*(y-1) and a can not be 11, so a=7 and b=11-a=4.