MathDB

gcd (d_1, n/d_2)=gcd (d_2, n/d_1) => d_1=d_2 , where d_1,d_2 pos. divisors of n

Source: 1998 Estonia National Olympiad Final Round grade 11 p1

March 11, 2020

number theorygreatest common divisorDivisors

Problem Statement

Let

d_1

and

d_2

be divisors of a positive integer

n

. Suppose that the greatest common divisor of

d_1

and

n/d_2

and the greatest common divisor of

d_2

and

n/d_1

are equal. Show that

d_1 = d_2