Grouping up Number theory-1
Number Theory
Level
3
Find the number of positive integers for which .
The answer is 34.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
We check that 2 is congruent to -1 mod 3. Hence we put that in n2^n + 1 and for even n we have 3 divides n + 1. We can easily find there are 17 such n below 100 starting from 2 and in multiples of 6. Again for odd n we use congruence mod 3 to get 3 divide -n + 1 =》 3 divides 2n + 1 then. We then find all these n starting with 1 and incresing in multiples of 6. We get 17 such n again. So no. Of sol. : 17+17 = 34.