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Perfect roots (Posted on 2024-10-28)

Find the smallest positive integer n, such that (5n)^1/5, (6n)^1/6, (7n)^1/7 are integers.

No Solution Yet Submitted by Danish Ahmed Khan

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re: solution

Comment 2 of 2 |

(In reply to solution by Charlie)

I got the same result without need of calculator.

The three roots have some nice patterns:

5^17 * 6^7 * 7^18

5^14 * 6^6 * 7^15

5^12 * 6^5 * 7^13

Posted by Jer on 2024-10-28 09:00:24

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