WebFeb 18, 2024 · It happens that $3$ has order $8\bmod 2^5=32$, so $$3^{1234567}\equiv 3^{1234567\bmod 8}=3^7\mod 2^5.$$ As to the congruence class $\bmod 5^5=3125$, we have $\varphi(5^5)=4\cdot 5^4=2500$, so $$3^{1234567}\equiv 3^{1234567\bmod 2500}=3^{2067}\mod 5^5.$$ This requires $11$ squarings and $3$ multiplications mod. … WebThe third planet from the sun, Earth is the only place in the known universe confirmed to host life. With a radius of 3,959 miles, Earth is the fifth largest planet in our solar system, …
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