+26367 How many whole numbers less than 18,632 are congruent to 23(mod 37)?
\(\begin{array}{|lrcll|} \hline & 18632 &\equiv& 23 \pmod {37} \\ & 18632 -23 &=& n\cdot 37 \\ & n &=& \dfrac{18632 -23}{37} \\ & n &=& 502.945945946 \quad | \quad 0 \le n \le 502 \\ \Rightarrow \text{There are } \mathbf{503} \text{ numbers}. \\ \Rightarrow \text{The lowest number is } 37\cdot 0 + 23 = 23 \\ \Rightarrow \text{The highest number is } 37\cdot 502 + 23 = 18597 \\ \hline \end{array} \)
