Compile a list of all square integers below 10,000, not terminating by zero, such that erasing their two last digits creates a new square number.
Any such number would be of the form (10a)^2 + b
where 1 <= b <= 99.
Then b would have to be chosen so that our number is (10a + 1)^2, or (10a + 2)^2 etc
For the first of these, b = 20a + 1, which means a<5 since b<100.
So the largest such number is less than 2500.
This means the list of numbers is complete.
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Posted by Larry
on 2021-05-18 10:10:13 |
the list is complete
