EASY
IOQM - PRMO and RMO
IMPORTANT
Earn 100

How many positive integers n are there such that 3n100 and x2n+x+1 is divisible by x2+x+1?

50% studentsanswered this correctly

Important Questions on Polynomials

HARD
IOQM - PRMO and RMO
IMPORTANT
Each of the numbers x1, x2, , x101 is ±1. What is the smallest positive value of 1ij101xixj ?
HARD
IOQM - PRMO and RMO
IMPORTANT
If x=2+3+6 is a root of x4+ax3+bx2+cx+d=0, where a, b, c, d are integers, what is the value of a+b+c+d ?
HARD
IOQM - PRMO and RMO
IMPORTANT
Find the number of positive integers less than 101 that cannot be written as the difference of two squares of integers.
HARD
IOQM - PRMO and RMO
IMPORTANT
Find the largest value of ab such that the positive integers a, b>1 satisfy abba+ab+ba=5329.
HARD
IOQM - PRMO and RMO
IMPORTANT
What is the smallest prime number p such that p3+4p2+4p has exactly 30 positive divisors?
HARD
IOQM - PRMO and RMO
IMPORTANT
The equation 166×56=8590 is valid in some base b10 (that is, 1, 6, 5, 8, 9, 0 are digits in base b in the above equation). Find the sum of all possible values of b10 satisfying the equation.
MEDIUM
IOQM - PRMO and RMO
IMPORTANT
Integers a, b, c satisfy a+b-c=1 and a2+b2-c2=-1. What is the sum of all possible values of a2+b2 +c2?
HARD
IOQM - PRMO and RMO
IMPORTANT
If a,b,c4 are integers, not all equal and 4abc=a+3b+3c+3, then what is the value of a+b+c ?