Perfect square?
Number Theory
Level
2
A postive integer has five distinct even digits. This number is a perfect square.
Is this possible?
Yes, it's possible.
No, it is not possible
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1 solution
There are five even digits: 0, 2, 4, 6 and 8. So if it possible, then the digits of the number are 0, 2, 4, 6, and 8 in some order. The sum of the digits is 20. Since 2 0 ≡ 2 m o d 3 , the number (if there is such a number) makes two remainder, when it is divided by 3. However a perfect square never makes 2 remainder, when it is divided by 3.
Therefore it is not possible.