5

Part of 2007 Cuba MO

Problems(1)

unique integer by digits 2,5 with 2007 digits, divisible by 2^{2007}

Source: 2007 Cuba MO 2.5

Prove that there is a unique positive integer formed only by the digits

2

5

2007

digits and is divisible by

2^{2007}

number theoryDigitsdividespower of 2