Unanswered Algebra Questions

Sorry double post correct link: http://targetiit.com/iit_jee_forum/posts/passage_on_matrices_2327.html ...

wrong post sorry ...

The integers a and b have the property that for every nonnegative integer n, the number 2^{n}a+b is the square of an integer. Show that a=0. ...

Suppose that p is a prime number and is greater than 3 . Prove that 7^{p}-6^{p}-1 is divisible by 43. ...

Find all positive integers, representable uniquely as \frac{x^{2}+y}{xy+1} where x and y are positive integers. ...

In a society of n people, any two persons who do not know each other have exactly two common acquaintances, and any two persons who know each other don’t have other common acquaintances. Prove that in this society every per ...

in expansion of 1/(1-ax)(1-bx) = a0 + a1x +... an then wat is an? ...

Prove that √(7/2) ≤ |1 + z| + |1 − z + z2| ≤ 3√(7/6) for all complex numbers with |z| = 1. ...

Find all polynomial P(x) with real coefficients satisfying P^2(x)+P^2(x-1)=2(P(x)-x)^2 ...

Prove that for positive real numbers a, b, c, d, we have \[ \frac{1}{\frac{1}{a}+\frac{1}{b}}+\frac{1}{\frac{1}{c}+\frac{1}{d}}\le\frac{1}{\frac{1}{a+c}+\frac{1}{b+d}} \] ...

Find all real values of parameter a for which the equation in x \[ 16x^{4}-ax^{3}+(2a+17)x^{2}-ax+16 = 0 \] has four solutions which form an arithmetic progression. ...

On a bookcase there are n ≥ 3 books side by side by different authors. A librarian considers the first and second book from left and exchanges them iff they are not alphabetically sorted. Then he is doing the same operation ...

Given six real numbers a,b c,x y,z , , such that 0<b-c<a<b+c and ax+by+cz=0. What is the sign of the sum ayz+bzx+cxy ? o promise u if u really try this question sincerely , you are bound to learn a new concept ...

a sum of rs/-1728 is distributed equally among some persons & each got 4/3times as many rs/- as dere r persons find d no. of persons ...

sum the series 1+ 1/2 + 1/3 + 1/4.......... i used integration ....but that doesn't help as log {0} doesn't exist .....please help.....please give an explanation with your answer ...

Q1 Let an=∫(1-cos2nx)/1-cos2x ,then a1,a2,a3 ...are in where limits of integration are 0 to π/2 Q2 Let an=∫sin2nx/sinx dx for all n≥0 and bn=an-an-1 for all n≥1.The sequence b1,b2,b3.. is in ??? where limits of integ ...

In five throws with single die what is the chance of throwing a) three aces exactly b) three aces atleast ...

1) The eqn (cos p -1) x2 + (cosp)x + sinp =0, in the variable x ,has real roots. Then p can have any value in the interval (a) (0 , 2 pie) (b) (- pie, 0 ) (c) (- pie/2 , pie/2 ) (d) ( 0 ,pie) ...

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1+( 2 -1)/2 2 +( 3-2 2 )/12+ (5 2 -7)/24 2 + (17-2 2 ) /80 +......∞ ...

http://www.ajorza.org/wimo/images/mathfiles/files/resources/intseq.pdf ...

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A nice question from a book I downloaded today..and I have become an addict Given a circle of n lights, exactly one of which is initially on, it is permitted to change the state of a bulb provided one also changes the state o ...

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