A STORAGE FOR THOUGHT

It turns out that 12 cm is the smallest length of wire that can be bent to form an integer sided right angle triangle in exactly one way, but there are many more examples.12 cm: (3,4,5) 24 cm: (6,8,10) 30 cm: (5,12,13) 36 cm: (9,12,15) 40 cm: (8,15,17) 48 cm: (12,16,20)In contrast, some lengths of wire, like 20 cm, cannot be bent to form an integer sided right angle triangle, and other lengths a..

문제를 볼까?For a prime p let S(p) = (∑(p-k)!) mod(p) for 1 ≤ k ≤ 5.For example, if p=7, (7-1)! + (7-2)! + (7-3)! + (7-4)! + (7-5)! = 6! + 5! + 4! + 3! + 2! = 720+120+24+6+2 = 872. As 872 mod(7) = 4, S(7) = 4.It can be verified that ∑S(p) = 480 for 5 ≤ p < 100.Find ∑S(p) for 5 ≤ p < 108.소수 p에 대해서 S(p) = (∑(p-k)!) mod(p) (1 ≤ k ≤ 5)라 정의하자. 예를 들자면 p가 7일 때 (7-1)! + (7-2)! + (7-3)! + (7-4)! + (7-5)! = 6!..