Question 117716

“Fermat's little theorem” can help you to determine whether number is prime or not. One version of the theorem states:

If {{{ p}}} is a {{{prime}}}{{{ number}}} and {{{b}}} any whole number, then {{{b^p – b}}} is a multiple of {{{ p}}} . 

Examples:	

 if {{{p = 7}}} and {{{b =2}}}, the theorem correctly predicts that {{{7}}} divides evenly into {{{2^7 – 2}}}, or {{{126}}}

{{{4^3 - 4 = 60}}} is divisible by {{{3}}} 

{{{7^2 - 7 = 42}}} is divisible by {{{2}}}

{{{(-3)^7 - (-3) = -2184}}} is divisible by {{{7}}}
 
{{{2^97 - 2 = 158 456 325 028 528 675 187 087 900 670}}} is divisible by{{{ 97}}}