+0  
 
+1
476
2
avatar+487 

What is the units digit of $2^{2^{1000}}+1$(The $1000^{th}$ Fermat prime)?

 Apr 5, 2021
 #1
avatar+605 
+2

Note that $2^{13}\equiv 2^1\pmod{10}$ so $2^{n}=2^{n+12}\pmod{10}$. Then $2^{1000}\equiv 4\pmod{12}$ so $2^{2^{1000}}\equiv 2^4\equiv 6\pmod{10}$. The answer is $6+1=7$.

 Apr 5, 2021
 #2
avatar+487 
0

Thank you, it was correct!

RiemannIntegralzzz  Apr 5, 2021

0 Online Users