INMO 1993 ugly question?

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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

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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

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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.....

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INMO 1993 ugly question?

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