INMO 1993 ugly question?

IIT JEE 2015 Papers › Olympiad Stuff questions › INMO 1993 ugly question?

Let p(x) = x²+ax+b be a quadratic polynomial. 'a' and 'b' belongs to integers. Prove that for any integer 'n' ,there is some 'm' such that P(n)P(n+1) = P(m)

Does this question have any good solution?

one can show that m = an + b+n(n+1) works..

#Mathematics #Olympiad Stuff

UP 0 DOWN 0 0 2
Post on FacebookPost anonymously?

2 Answers

341

Hari Shankar ·2011-07-12 04:22:49

Here's something i tried some years ago:

http://www.goiit.com/posts/list/algebra-quadratic-equations-question-72461.htm#357130

UP 0 DOWN 0
Post on FacebookPost anonymously?

Shubhodip ·2011-07-12 04:47:08

That is great .....

Pleasure to read...

I simply hit at the expression.

terms like b², 2abn ,a²n² , n²(n+1)² give enough hint...

But yours is the only one that can fetch full marks i guess.....

UP 0 DOWN 0
Post on FacebookPost anonymously?

Your Answer

Basic Integral Calculus Operators Symbols Matrix Cases

√ √ || {} [] () → ~ ^ x x x → → ln log lg lim lim cos sin tan cot arcsin arccos arctan

∫ ∫ ∫ ∫ ∫ ∬ ∬ ∬ ∬ ∬ ∭ ∭ ∭ ∭ ∭ ⨌ ⨌ ⨌ ⨌ ⨌

∑ ∑ ∑ ∑ ∑ ∮ ∮ ∮ ∮ ∮ ∏ ∏ ∏ ∏ ∏ ∐ ∐ ∐ ∐ ∐

+ - × ÷ ± ∓ = ∪ ∩ ≠ ∼ ≈ ∅ ∀ ∃ ∈ ∋ ∝ ≤ ≥ ≃ ≅ ≡ < > ≪ ≫ ⊂ ∉ ⊃ ⊆ ⊇ ⇒ ⇐ ⇔ ⇒ ⇐ ⇔ ⇑ ⇓ ⇕ → ← ↔ → ← ↔ ↑ ↓ ↕ ↖ ↗ ↘ ↙ ↪ ↩ ⇀ ↼ ⇁ ↽

° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω

Close [X]

INMO 1993 ugly question?

2 Answers

Your Answer

Add Image

Similar Questions