Quiz on Modular Arithmetics

Euler-Phi: $\varphi(10) = 4$. Der Exponent $402 = 100 \cdot 4 + 2$. Also $3^{402} \equiv 3^2 = 9 \pmod{10}$.

$R_{25}(26^{2024}) = R_{25}(1^{2024}) = 1$

$R_{11}(10^{10}) = R_{11}((-1)^{10}) = 1$

$R_{50}(49^{3}) = R_{50}((-1)^{3}) = -1 = 49$

$R_{7}(2^{300}) = R_{7}((2^3)^{100}) = R_{7}(8^{100}) = R_{7}(1^{100}) = 1$