MathDB

1

Part of 2001 Iran MO (2nd round)

Problems(2)

1+np - Iran NMO 2001 (Second Round) - Problem1

Source:

10/4/2010
Let nn be a positive integer and pp be a prime number such that np+1np+1 is a perfect square. Prove that n+1n+1 can be written as the sum of pp perfect squares.
number theory proposednumber theory
P(x) Polynomial - Iran NMO 2001 (Second Round) - Problem4

Source:

10/4/2010
Find all polynomials PP with real coefficients such that ∀x∈R\forall{x\in\mathbb{R}} we have: P(2P(x))=2P(P(x))+2(P(x))2. P(2P(x))=2P(P(x))+2(P(x))^2.
algebrapolynomialalgebra proposed