MathDB

4

Part of 2011 Dutch IMO TST

Problems(2)

find n such P(x) = 3x^3-nx-n-2 can be product of integer polynomials

Source: Dutch IMO TST1 2011 p4

1/10/2020
Determine all integers nn for which the polynomial P(x)=3x3−nx−n−2P(x) = 3x^3-nx-n-2 can be written as the product of two non-constant polynomials with integer coeffcients.
polynomialInteger Polynomialalgebra
prime sequence, p_k = 2p_{k-1} + 1 or p_k = 2p_{k-1} - 1

Source: Dutch IMO TST2 2011 p4

1/10/2020
Prove that there exists no in nite sequence of prime numbers p0,p1,p2,...p_0, p_1, p_2,... such that for all positive integers kk: pk=2pk−1+1p_k = 2p_{k-1} + 1 or pk=2pk−1−1p_k = 2p_{k-1} - 1.
recurrence relationSequenceprime numbersnumber theory