3

Part of 2012 Brazil National Olympiad

Problems(1)

n^k ends in a 2012-string of 1's

Source: Problem 3, Brazilian MO, 2012

Find the least non-negative integer

n

such that exists a non-negative integer

k

such that the last 2012 decimal digits of

n^k

1

modular arithmeticinductionnumber theory unsolvednumber theory