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

Source:

July 9, 2024

algebranumber theory

Problem Statement

The first five terms of a sequence are

1, 2, 3, 4

and

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)