2023 AMC 10B Problem 14 - Math Gold Medalist

Lor

2023 AMC 10B

Problem 14

How many ordered pairs of integers $(m,n)$ satisfy the equation $m^2+mn+n^2 = m^2n^2$ ?

$\textbf{(A) }7\qquad\textbf{(B) }1\qquad\textbf{(C) }3\qquad\textbf{(D) }6\qquad\textbf{(E) }5$

Related Ideas

ab=x^2 or ab=px^2 (p is prime)

Greatest Common Divisor

Important Identities

Hint

(m+n)^2 = mn(mn+1)

gcd(mn, mn+1)=1

mn and mn+1 are perfect squares