Maths Olympiad Daily Problems

How many of you guys wrote CMI today?

F(x)= ax² +bx +c Given F(-1)>=4 F(1)<=0 F(3)>=5 Find the least value of a

Pls anyone can solve this and send me the solution?

Find the values of (a, b, c) such that the polynomial: x^4 + ax^3 + 3bx^2 + bx + c is the fourth power of another polynomial.

Lets f(x) and g(x) be monic integer polynomoals such that f(a)/equiv g(a+m_p) (mod p) For infinitely many a in non negative integers Then prove that for some rational r f(x)=g(x+r)

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QUESTION- So this is a game in which 2 players are playing You are blindfolded and the other player which we can call the host of the game is not blindfolded, in front of You there are 4 cylinders kept on the 4 corners of a table. Inside each cylinder there is an arrow, it can be pointing upwards or downwards, our task is to make all the arrows in the same orientation either up or down, conditions are we can only touch 2 cylinders in a move, we can't feel the direction of the arrow, we can either flip one cylinder or 2 cylinders or we can leave the board as it is but it will be counted as a move, what the host will do is that after your each move he can turn the board horizontally in any multiple of 90 degrees... once all the arrows are in same orientation (up or down) the game host will tell us that we have won, now we have to find a strategy which confirms that after certain moves we will definitely win.

the first real research in mathematics by ai and a lot more to come. we are entering a new era i think.

https://chatgpt.com/share/69dd1c83-b164-8385-bf2e-8533e9baba9c Chat gpt proved a 60 year old erdos conjecture. the user shared link in X and reddit. check out the above . Chat gpt 5.4 took 1 hour 20 minutes to the proof.

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