5

Part of 2016 Argentina National Olympiad

Problems(1)

min p, smallest prime divisor of n when s=a+b=a^2+b^2=m/n

Source: 2016 Argentina OMA Finals L3 p5

a

b

be rational numbers such that

a+b=a^2+b^2

. Suppose the common value

s=a+b=a^2+b^2

is not an integer, and let's write it as an irreducible fraction:

s=\frac{m}{n}

p

be the smallest prime divisor of

n

. Find the minimum value of

p

number theoryprime divisorsdivisoralgebra