Problem 60945. Compile evidence for the Carmichael totient conjecture

The totient function phi(n) counts the positive integers up to n that are relatively prime to n. The Carmichael totient conjecture states that for every integer there is a different integer with the same value of the totient.
For example, the totient of 4 is 2, which is also the totient of 3 and 6. The totient of 17 is 16, which is also the totient of 32, 34, 40, 48, and 60.
Not all numbers can be totients: no odd numbers greater than 1 are totients, and an infinite number of even numbers are non-totients. However, the conjecture states that for all numbers that are totients, they are shared by at least two integers.
Write a function that takes a value x and returns the two smallest integers with a totient of x.
Solve

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100.0% Correct | 0.0% Incorrect
Last Solution submitted on Jul 21, 2025

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conjecture number theory

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