AMC 10A 2024 (Problem 11)How many ordered pairs of integers (m,n)(m, n)(m,n) satisfy n2−49=m\sqrt{n^2 - 49} = mn2−49=m ?(A) 1\text{(A)}\;1(A)1(B) 2\text{(B)}\;2(B)2(C) 3\text{(C)}\;3(C)3(D) 4\text{(D)}\;4(D)4(E) infinitely many\text{(E)}\;\text{infinitely many}(E)infinitely manyRelated TopicsToolkit 10 — Difference of squaresHints (4)Hint 1Square both sides.Hint 2Rearrange and use Identity 10 (Difference of Squares).Hint 3n2−m2=(n−m)(n+m)=49n^2 - m^2 = (n - m)(n + m) = 49n2−m2=(n−m)(n+m)=49.Hint 4n−mn - mn−m and n+mn + mn+m are factors of 49.Final Answer(B) 2