Let n~ be defined for all positive integers n as the remainder when (n - 1)! is divided by n.
What is the value of 31~ ?
Select the correct option.
A) 2 B) 1 C) 0 D) 8 E) 31
n~ = (n-1)!   so 31~ = (31-1)= 
<gadget id="calculator">(31-1)</gadget>
<output>30</output>
30!   when 30!/31 we have 16*2 inside 30!   hence 31 gets cancelled and we get remainder as 0   0
<result>C</result>
Let n~ be defined for all positive integers n as the remainder when (n - 1)! is divided by n.
What is the value of 31~ ?