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Somudro Gupto
Somudro Gupto
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Relation between exponents to the different bases over $\mathbb{Z}^p$^\times_p$?

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Somudro Gupto
Somudro Gupto
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This question is similar to this question, Relation between elements with fixed exponent over different $\mathbb{Z}^\times_p$

For all primeseach prime $p$ that havehas a primitive root $3$ and for all $a\in\mathbb{Z}^+$, there exists a $b\in\mathbb{Z}^+$ such that $2^a \equiv 3^b \pmod{p}$. Is there any relation between $a$ and $b$ that can be expressed without $p$? If not then is there one for the primes with a primitive root $5$?

This question is similar to this question, Relation between elements with fixed exponent over different $\mathbb{Z}^\times_p$

For all primes $p$ that have a primitive root $3$ and for all $a\in\mathbb{Z}^+$, there exists a $b\in\mathbb{Z}^+$ such that $2^a \equiv 3^b \pmod{p}$. Is there any relation between $a$ and $b$ that can be expressed without $p$? If not then is there one for the primes with a primitive root $5$?

This question is similar to this question, Relation between elements with fixed exponent over different $\mathbb{Z}^\times_p$

For each prime $p$ that has a primitive root $3$ and for all $a\in\mathbb{Z}^+$, there exists a $b\in\mathbb{Z}^+$ such that $2^a \equiv 3^b \pmod{p}$. Is there any relation between $a$ and $b$ that can be expressed without $p$? If not then is there one for the primes with a primitive root $5$?

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Somudro Gupto
Somudro Gupto
  • 1
  • 2

Relation between exponents to the different bases over $\mathbb{Z}^p$?

This question is similar to this question, Relation between elements with fixed exponent over different $\mathbb{Z}^\times_p$

For all primes $p$ that have a primitive root $3$ and for all $a\in\mathbb{Z}^+$, there exists a $b\in\mathbb{Z}^+$ such that $2^a \equiv 3^b \pmod{p}$. Is there any relation between $a$ and $b$ that can be expressed without $p$? If not then is there one for the primes with a primitive root $5$?