(429) 6

Part of 1994 Tournament Of Towns

Problems(1)

TOT 429 1994 Autumn A J6 sum a_i^6 = product a_i

Source:

The sum of sixth powers of six integers minus

1

is six times greater than the product of these six integers. Prove that one of them is

1

-1

and all others are

0

s.
(LD Kurliandchik)