Number theory

JEE Mains Coaching › Fundamentals questions › Number theory

*Prove that every integer of the form n^4+4 is always composite.........

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souvik seal ·2010-06-10 02:07:16

anirban r u sure u have posted the prob right
i think u have tried to give sophie germein identity which tells n^4+4 is composite always,,,its prof is very easy

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Anirban ·2010-06-10 02:59:17

Ya,Sorry,I typed it wrong..

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souvik seal ·2010-06-10 09:14:55

(n^2)^2+4=(n^2+2)^2-4n^2=(n^2+2++2n)(n^2+2-2n)...
hope u got the solution,,,,look any of the factor can not be 1...prove it!

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Lokesh Verma ·2010-06-14 04:05:45

There is a better generalization that we had done and has been asked in some olympiad too..

n⁴+4ⁿ is always composite.. if n>1

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souvik seal ·2010-06-14 06:04:23

that came once in isi entrance,,,too simple...na

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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

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Number theory

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