18

Part of 2005 Baltic Way

Problems(1)

z must have a factor congruent to 3 (mod 4)

Source: Baltic Way 2005

x

y

be positive integers and assume that

z=\frac{4xy}{x+y}

is an odd integer. Prove that at least one divisor of

z

can be expressed in the form

4n-1

n

is a positive integer.

modular arithmeticnumber theory proposednumber theory