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发帖数: 332 | | f*******n
发帖数: 12623 | 2 It's a multiple of 5, so 5 is a factor. Any number x has 1 and x as factors.
We also know that 5 and x/5 are factors. So those are the four factors (1,
5, x/5, and x). This also means that x/5 is prime; otherwise there would be
more factors.
The factors can be written using only two digits (which must be 1 and 5). So
both x and x/5 are written using only 1 and 5. x is a multiple of 5, so
must end in 5 or 0 -- but it can't be 0, so it ends in 5. Since x/5 is prime
and it is not 5, it can't end in 5 (which would make it a multiple of 5 and
not prime), so it ends in 1.
x is the square root of a 4 digit number, so it must be between sqrt(1000) =
31.2 and sqrt(9999) = 99.9.
What are the choices for x/5? It ends in 1. It can't be 1, so it must be 2-
digit. So it must be 11 or 51. 51 is not prime and 51 * 5 would be too big
anyway. So x/5 = 11. And x = 55. |
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