Number Theory Help: Showing 25 is Strong Pseudoprime to Base 7

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SUMMARY

The discussion focuses on demonstrating that 25 is a strong pseudoprime to base 7 using Miller's test. The user suggests an efficient approach by calculating \(7^{25} \mod 25\) and highlights the importance of modular arithmetic to prevent large exponentiation. The calculation shows that \(7^2 \equiv -1 \mod 25\) and leads to the conclusion that \(7^{24} \equiv 1 \mod 25\), confirming 25's status as a strong pseudoprime to base 7.

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I'm trying to show that 25 is a strong pseudoprime to the base 7 using millers test. Is there a better way to solve this than just brute force?
Thanks
 
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I'm not sure of the notation. I assume that you need to compute

[tex]7^{25}\;\;\textrm{mod}\;(25).[/tex]

The way to do is to avoid letting the power get all out of control. Consider:

7*7 = 49 = 24 = -1 mod (25)

so
7*7*7*7 = 1 mod (25).

so what is 7^{24}?

Carl
 

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