∵xn−yn=(x−y)[xn−1+xn−2y+xn−3y2+......+yn−1] xn−yn is divisible by x−y Stat 1→(2023)2022−(1999)2022 (2023)−(1999)=24 Stat 2→(2023)2022−(1999)2022 is divisible by 8 13(1+12)n−11n−13 13[1+nC1,(12)+nC2(12)2+...]−11n−13 ⇒(156n−11n)+13⋅nC2(12)2+13⋅nC3(12)3+... ⇒145n+13⋅nC2(12)2+13⋅nC3(12)3+... If (n=144m,m∈N) then it is divisible by 144 for infinite values of n. Ans. Option 4