Problem 2. (a). Consider the sequence of integers of the form p4-1, where p > 5 is a prime number. So the sequence looks

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Problem 2 A Consider The Sequence Of Integers Of The Form P4 1 Where P 5 Is A Prime Number So The Sequence Looks 1 (51.94 KiB) Viewed 34 times

Problem 2. (a). Consider the sequence of integers of the form p4-1, where p > 5 is a prime number. So the sequence looks like: (74 — 1), (11+ — 1), (134 — 1),..., (p+ — 1),.... Find the greatest common divisor of this sequence of integers. (b). Let m > 1, k> 1 be integers. We define Am = 1¹ +2k +3k +...+ m². (i). Show that if k is odd, then m+1 divides jk +(m+1−j)k for all j≥ 1. (ii). Suppose m is even and k is odd, use part(i) to show that A = 0 (mod m + 1). (iii). Find all possible values of even m's and odd k's for which Am is a prime number.