1,6k4 is a 4-digit number.

So, 1^4 + 6^4 + k^4 + 4^4 = 16k4

Evaluate: 1 + 1296 + k^4 + 256 = 16k4

Simplify: 1553 + k^4 = 16k4

Whatever k is, it must be the case that the UNITS digit of k^4 is 1, so that 1553 + k^4 = 16k4

Test some values..

k =1: 1^4 = 1, so we get: 1553 + 1 = 1614 NO GOOD

k =3:3^4 = 81, so we get: 1553 + 81 = 1634 WORKS!!

Answer: k = 3

Cheers,

Brent