A number theory problem by A Former Brilliant Member
Number Theory
Level
3
How many positive integers less than 10000 have an odd number of positive factors?
none of these
21
100
99
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1 solution
The only positive integers that have an odd number of factors are perfect squares. The largest perfect square less than 1 0 0 0 0 is 9 9 , 9 9 2 = 9 8 0 1 . So the answer is 9 9 .