5

Part of 1998 Baltic Way

Problems(1)

Multiple of 2^n has only digits a and b

Source: Baltic Way 1998

a

be an odd digit and

b

an even digit. Prove that for every positive integer

n

there exists a positive integer, divisible by

2^n

, whose decimal representation contains no digits other than

a

b

modular arithmeticinductionnumber theory proposednumber theory