SOLUTION: Set A consists of all integers a such that a = p2 � 1, where p is a prime greater than 3. What is the greatest common factor of all the numbers in set A?

Question 1033719: Set A consists of all integers a such that a = p2 � 1, where p is a prime greater than 3. What is the greatest common factor of all the numbers in set A?
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
==> either p-1 or p+1 is divisible by 3, since in any three consecutive natural numbers {p-1, p, p+1}, one of them is divisible by 3, and definitely it is not p because it is prime.
Also, p being a prime greater than or equal to 5 means it is an odd number and should be of the form p = 2k+1.
==> .
The expression 4k(k+1) has two factors that are consecutive numbers, hence one of them has 2 as a factor.
==> 8 divides .
==> 3*8 = 24 is common factor of all numbers a. Since , it also makes it the greatest common factor.

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