(468) 2

Part of 1995 Tournament Of Towns

Problems(1)

TOT 468 1995 Autumn J A2 product of the first 70 terms = sum of squares

Source:

The first five terms of a sequence are

1, 2, 3, 4

5

. From the sixth term on, each term is

1

less than the product of all the proceeding ones. Prove that the product of the first

70

terms is equal to the sum of their squares.
(LD Kurliandchik)

algebranumber theory