39lets see how many guys recognise the standardness of the question.. u too stay away ,, :P
and sorry for not mentioning your name above :P :D
Let P(x) be a polynomial with integral coefficients. Prove that we can never have
P(a) = b and P(b) = c and P(c) = a where a,b and c are integers.
( bhatt sir , please stay away)
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8 Answers
62this is a standard question..
Am I allowed ? :P
*even i have learnt a lot due to prophet sir :)
3962it is ok...
Prophet sir is in a different league... [1]
Even i am his student :)
39no one seems so interested in this...
nishant bhaiyan pull it off...
62btw for this question.. i did not post the solution to this one because i had seen the solution in Problem solving strategies and not solved it myself...... (That is one book i have started to love like anything)
and I called it standard because you had posted the question.. otherwise it is a fairly difficult one for a JEE aspirant... [3]
39:P
so late with arthur enge?? but anyways any time is good time..
that book is such a thing where people easily recognise the questions if posted anywhere.....
an awesome book
9trick involved is to see P(P(P(x)))=x has atleast 3 integral solutions
a,b,c same then p(x) = x
P(3)(x) - x =(x-a)(x-b)(x-c)g(x)