Decimal expansion
= Decimal expansion
{title2=$M=\sum_{i=0}^s a_i10^i$}
A nonnegative integer's <decimal expansion> uses digits $0\leq a_i\leq9$. Testing divisibility reduces this polynomial in ten modulo the divisor: for example $10\equiv-1\pmod{11}$ makes divisibility by eleven equivalent to vanishing of the alternating digit sum.