Show that the product of two consecutive numbers cannot be a perfect square

#maths #imo #iitjee #mathematics #square

[@Nayeem_5052]

Sir I have a prove that type question of Recurrence Relation that I am unable to solve, can u solve it and make a video on it. Question is : Given, F1 = 0 F2 = 1 F3 = 3 F4 = 4 Fn = Fn-1 + Fn-3 + Fn-4, for any natural number n >= 5 For example, F5 = F5-1 + F5-3 + F5-4 = F4 + F2 + F1 = 4 + 1 + 0 = 5 Prove that sqrt(F2p) = sqrt(F2p-2) + sqrt(F2p-4) for any natural number p >=3 . Can u please prove this, u can verify the question by checking the values till around F16, they will always follow this pattern.

[@Mathematica1997]

Well I'm not familiar with recurrence relation now, but soon I'll learn and definitely will try to make a video on it. Thank you for your suggestion 😊