1

Part of 1996 India National Olympiad

Problems(1)

Source: INMO 1996 Problem 1

a) Given any positive integer

n

, show that there exist distint positive integers

x

y

x + j

y + j

j = 1 , 2, 3, \ldots, n

; b) If for some positive integers

x

y

x+j

y+j

for all positive integers

j

x = y

modular arithmeticnumber theory solvednumber theory