Consider the numbers 51,87 and 115.
Now 51*87*115 = 510255 and [lcm(51-1 ,87-1, 115-1)= 122550
and 2^122550 = 104869 (mod510255)
Let D = gcd(104869 - 1,510255)
Is D divisible by 51, 87 or 115?
What can we conclude in terms of the primality of these three integers, if they don't divide D?