61. Determine the remainder of the division by 7 of the number

$$
3^{100}
$$

The 10-arithmetic and 7-arithmetic we have discussed are special cases of residue arithmetic modulo $m$, or $m$-arithmetic. Let $m$ be any positive integer. The elements of $m$-arithmetic are the numbers $0,1,2, \ldots, m-1$. Addition and multiplication in $m$-arithmetic are defined as follows: to add (or multiply) two numbers, one must take the remainder of the division by $m$ of their ordinary sum (respectively product).
61. Let's compute $3^{100}$ in 7-arithmetic:

$$
3^{2}=2,3^{8}=6,3^{4}=4,3^{5}=5,3^{6}=1
$$

Therefore,

$$
3^{100}=3^{6 \cdot 16+4}=\left(3^{6}\right)^{16} \cdot 3^{4}=3^{4} \Rightarrow 4
$$

$14^{*}$