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Albert1
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given $9^{40}$ mod 100=1
if $A=9^9$
find $9^A $ mod $100=?$
if $A=9^9$
find $9^A $ mod $100=?$
we can computeAlbert said:given $9^{40}$ mod 100=1
if $A=9^9$
find $9^A $ mod $100=?$
The value of A can be found by taking the logarithm of both sides of the equation. This will give us the equation A*log(9) = log(1) = 0. Since log(9) = 2, A must be equal to 0.
Yes, you can use a calculator to solve this equation. Just remember to use the logarithm function to find the value of A.
Yes, there is a faster way to solve this equation. You can use the properties of modular arithmetic to simplify the equation. For example, since 9 and 100 are relatively prime, we can use Euler's theorem to rewrite the equation as $9^{\phi(100)}$ mod 100 = 1, where $\phi$ is the Euler totient function. Since $\phi(100) = 40$, we can see that A must be equal to 1.
In this case, we can still use the properties of modular arithmetic to find the value of A. For example, if A is a fraction, we can use the Chinese Remainder Theorem to find the value of A mod 100. This will give us a unique solution for A.
Yes, this method can be applied to other modular equations as well. However, it may not always give a unique solution for A. In some cases, there may be multiple solutions or no solutions at all. It is important to check the properties of modular arithmetic before using this method to solve an equation.