Find n

I found this problem on You Tube.
Find n.

 

cool

 

1. Can you find n?

2. Did you see my new threads in the Algebra Forum here?

 

to find n you can just guess , there is no exact formula to calculate n
first guess is that n must be even and greater than 133

using modular algebra

133^5 ≡ 3mod10
since n^5> 133^5 it means that n > 133
n^5≡ 4mod10

Integers congruent to 4mod10:

14, 24, 34, 44, 54, 64, 74, 84, 94, 104, 114, 124, 134, 144, 154, 164, 174, 184, 194, 204, ...
since n > 133 we can use 144, 154, 164, 174, 184, 194, 204, ...
trying 144 shows us it is a solution

 

Did you see my threads in this Algebra forum?

 

which ones?

 

You found my new threads.