Question 613270
In base, the number 31 represents a prime number. In base k, however, this two-digit number represents a perfect square. For what value or values of k, 3< k <10, is 31 a perfect square?
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Assuming you mean base 10:
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Bases 2 & 3 are eliminated by the 3.
For bases 4 to 9, 31 = 3*b + 1, b is the base
4: 13
5: 16
6: 19
7: 22
8: 25
9: 28