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A square (Posted on 2004-06-25) Difficulty: 2 of 5
A number AABB is the square of an integer. Find this integer, aided by pen and paper. No other calculating aids allowed.

See The Solution Submitted by Ady TZIDON    
Rating: 3.1429 (7 votes)

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Squares, squares... | Comment 9 of 15 |

A number AABB may be written as 11*(100A + B), where A and B are integers between 1 and 9.
If 11*(100A+B) is a square, then 100A+B must be divisible by 11. Indeed, (100A+B)/11 must be a square, too.
If we take A = 7 and B = 4, then 100A+B = 704 = 11*64 = 11*(8^2).
(I've tried some values and noticed that 7 and 4 would satisfy the conditions.)
In fact, we have 7744 = 88^2.

 


  Posted by Elisabeth on 2004-06-28 19:36:09
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