Olympiad workbookIOQMComplex Number
How many positive integers n are there such that 3 n 100 and x^ 2^n +x+1 is divisible by x^2+x + 1 ?
Correct answer
49
Step-by-step solution
Since and ^2 are factors of X ^2+ X +1 ; so and ^2 will be factors of X ^ 2 n + X +1 2^n must be of the form 3 k+2 ; k I . For this to happen, n must be odd. So n = 3,5,7, 99 Number of such numbers =49