Special-250 Square
Number Theory
Level
2
A Special-250 Square is a 250 digit square number with 49 of the digits '9', 43 of the digits '4', 5 of the digits '1' and rest of the digits are all same (can be even '1', '4', '9'). How many Special-250 Square can be there?
The answer is 0.
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1 solution
The sum of the digits is 4 9 ⋅ 9 + 4 3 ⋅ 4 + 5 ⋅ 1 + 1 5 3 ⋅ x for some x . This simplifies to 6 1 8 + 1 5 3 x , which is divisible by 3 but not 9 . So the number is divisible by 3 but not 9 , which is impossible for a perfect square.