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Prove that if p is a prime number greate...

Prove that if p is a prime number greater than 2, then the difference `[(2+sqrt(5))^p]-2^(p+1)` is divisible by p, where [.] denotes greatest integer.

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ARIHANT MATHS-BIONOMIAL THEOREM-Exercise (Subjective Type Questions)
  1. Determine the term independent of a in the expansion of ((a+1)/(a^(2/...

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  2. If in the expansion of (1+x)^n ,a ,b ,c are three consecutive coeffici...

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  3. Find n in the binomaial [ root (3)(2) + (1) /root(3)(3)]^(n) , if ...

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  4. if Sn = C0C1 + C1C2 +...+ C(n-1)Cn and S(n+1)/Sn = 15/4 then n is

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  5. C1/C0+2C2/C1+3C3/C2+............+nCn/C(n-1)=(n(n+1))/2

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  6. Find the term in (a/(sqrt(b))3+sqrt(b/(a3)))^(21) which has the same p...

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  7. The coefficient of x^r[0lt=rlt=(n-1)] in lthe expansion of (x+3)^(n-1)...

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  8. Prove that if p is a prime number greater than 2, then the difference ...

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  9. Integer just greater tehn (sqrt(3)+1)^(2n) is necessarily divisible by...

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  10. Solve the equation ""^(11)C(1) x^(10) - ""^(11)C(3) x^(8) + ""^(11)...

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  11. If (1 + x)^(n) = C(0) + C(1) x + C(2) x^(2) + …+ C(n) x^(n) , find th...

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  12. Evaluate sum(0 le i lne j le 10) ""^(21)C(i) * ""^(21)C(j).

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  13. Find the coefficient of x^4 in the expansion of (1+x+x^2+x^3)^(11)dot

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  14. Find the coefficients of x^(4) in the expansions of (2 - x + 3x^(2...

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  15. If for z as real or complex, (1+z^2+z^4)^8=C0+C1z2+C2z4++C(16)z^(32)t ...

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  16. If for z as real or complex . (1+z^(2) + z^(4))^(8) = C(0) C(1) z^...

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  17. Let f(x) = a(0) + a(1)x + a(2)x^(2) + …+ a(2n) x^(2n) and g(x) = b...

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  18. If a0,a1,a2,.... be the coefficients in the expansion of (1+x+x^2)^n ...

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  19. If a(0), a(1), a(2),… are the coefficients in the expansion of (1 ...

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  20. If a(0), a(1), a(2),… are the coefficients in the expansion of (1 ...

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