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Question:

1-Let $a,b$ be integers having the property that for any prime power $t$ there exists an integer $v_t$ such that $$ b\equiv a^{v_t}\pmod t. $$ Then there exists an integer $v$ such that $$ b=a^v. $$

2-Does it hold with $t$ being primes not prime powers?

thanks!

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  • $\begingroup$ Hensel's Lemma might help $\endgroup$ – Dr. Mathva Apr 7 at 15:34
  • $\begingroup$ What are your thoughts on the question? What have you tried and where did you get stuck? Is there more context to this problem? Did you find it in a book? Do you know Hensel's lemma? $\endgroup$ – Servaes Apr 7 at 16:39
  • $\begingroup$ @Servaes, it is a theorem in a book about sieve methods, but I would like to know if there are more elementary way to solve it. $\endgroup$ – asad Apr 7 at 20:00

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