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# help

+1
253
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How many whole numbers less than 18,632 are congruent to 23(mod 37)?

Feb 11, 2019

#1
0

37n + 23 < 18,632

n =502

Feb 11, 2019
#2
+24859
+5

How many whole numbers less than 18,632 are congruent to 23(mod 37)?

$$\begin{array}{|lrcll|} \hline & 18632 &\equiv& 23 \pmod {37} \\ & 18632 -23 &=& n\cdot 37 \\ & n &=& \dfrac{18632 -23}{37} \\ & n &=& 502.945945946 \quad | \quad 0 \le n \le 502 \\ \Rightarrow \text{There are } \mathbf{503} \text{ numbers}. \\ \Rightarrow \text{The lowest number is } 37\cdot 0 + 23 = 23 \\ \Rightarrow \text{The highest number is } 37\cdot 502 + 23 = 18597 \\ \hline \end{array}$$

Feb 11, 2019