MathDB

at most one of 2^{2^n}+ 1 and 6^{2^n}+ 1 is prime

Source: 12th or 13th QEDMO problem 6 (11. - 15. 12. 2013) https://artofproblemsolving.com/community/c2400093_2013_qedmo_13th_or_12th

July 5, 2021

number theoryprime

Problem Statement

A composite natural number

n

is called happy if at most one of the numbers

2^{2^n}+ 1

and

6^{2^n}+ 1

is prime. Show that there are infinitely many happy numbers.