What's the logic behind this property

egal said:
View attachment 30947
How does this work?
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The digit sum as described here is what we use in "casting out nines", which you can look up; it's the residue modulo 9. You can confirm the claim by finding the squares of each possible number (mod 9), which all turn out to be 1, 4, 7, or 9.

You haven't said anything about what you know about number theory, or where this question came from, so I have no idea whether what I have said will be enough.
 
Dr.Peterson said:
The digit sum as described here is what we use in "casting out nines", which you can look up; it's the residue modulo 9. You can confirm the claim by finding the squares of each possible number (mod 9), which all turn out to be 1, 4, 7, or 9.

You haven't said anything about what you know about number theory, or where this question came from, so I have no idea whether what I have said will be enough.
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It was enough, thanks a lot
 
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