1

Part of 2017 Irish Math Olympiad

Problems(2)

min multiple of 99 with digits 1 or 2

Source: Irish MO 2017 paper 1 problem 1

Determine, with proof, the smallest positive multiple of

99

all of whose digits are either

1

2

number theorymultipleDigits

n+1 is divisible by 5 , 2^n + n and 2^n -1 are coprime

Source: Irish MO 2017 paper 2 problem 1

Does there exist an even positive integer

n

n+1

is divisible by

5

and the two numbers

2^n + n

2^n -1

coprimedivisiblenumber theory