BMO1 2016/2017 (Problem 3)Determine all pairs (m,n)(m,n)(m,n) of positive integers which satisfy the equation n2−6n=m2+m−10n^2 - 6n = m^2 + m - 10n2−6n=m2+m−10.Related TopicsToolkit 6 — Square of a sumToolkit 7 — Square of a differenceToolkit 10 — Difference of squaresHints (4)Hint 1Use 6. Squares of a sum, 7. Squares of a difference and 10. Difference of squaresHint 2(n−3)2−9=(m+12)2−14−10(n-3)^2 - 9 = (m+\tfrac{1}{2})^2 - \tfrac{1}{4} - 10(n−3)2−9=(m+21)2−41−10Hint 35=(2m+1)2−(2n−6)2=(2m+2n−5)(2m−2n+7)5 = (2m+1)^2 - (2n-6)^2 = (2m+2n-5)(2m-2n+7)5=(2m+1)2−(2n−6)2=(2m+2n−5)(2m−2n+7)Hint 42m+2n−52m+2n-52m+2n−5 and 2m−2n+72m-2n+72m−2n+7 are factors of 555Final Answer(m,n)=(1,2), (1,4)(m,n) = (1,2),\ (1,4)(m,n)=(1,2), (1,4)