Changing from Base 11 to Base 10, the equation becomes:
x^2 - 18x + 80 = (x-8)(x-10)
Answer: Base 11, Roots are (8,10)
I ran a program similar to Charlie's, but I let the base vary from 2 up to 20000. There were no solutions for base larger than 11. Of course it doesn't make sense to have a base less than or equal to the largest digit, which is 7.
But I found a spurious result that in Base 3, (if you could have 3s and 7s in Base 3), there is a solution with integer roots.
Changing from Base 3 to Base 10, the equation becomes:
x^2 - 10x + 24 = (x-4)(x-6)
Answer: Base 3, Roots are (4,6)
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Posted by Larry
on 2023-02-07 09:12:19 |
Solution
