Here is a similar example: Suppose you want to find x where (0 £ x £ 100) and 17¹³ º x mod 101. As 17¹³ is too large for most calculators to show exactly we start with 17⁶=24137569 and, first dividing this by 101, we find that 17⁶=(238985)(101)+84 so we now know that 17⁶ º 84 mod 101.

The next step is to use this to tackle 17¹³.

1713 =(176)2 ×17 º 842 ×17 º 119952 mod 101 119952 =1187×101 + 65 º 65 mod 101.

Hence x=65.