Aesthetic square
Number Theory
Level
3
If is a 4-digit integer that is also a perfect squares , what is the value of ?
The answer is 11.
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1 solution
aabb
so it is 1000 a + 100 a + 10 b + b = 1100 a + 11 b = 11(100 a + b)
now for it to be a perfect square 100 a + b has to be divisible by 11 and so
a + b has to be divisible by 11 so 11 as sum of 2 digits maximum 18