Find the remainder when :121^n-25^n+1900^n-(-4^n) /2000

We know that 2000 = 16.25, hence we prove that both 16 and 25 divide it makiing the use of fact that (a-b) divides (aⁿ – bⁿ).
16 divides 121ⁿ-25ⁿ +1900ⁿ-(-4ⁿ):
Now, (121-25) / (121ⁿ-25ⁿ) ⇒ 96/ (121ⁿ-25ⁿ)
⇒ 16/ (121ⁿ-25ⁿ)
Now, (1900-(-4)) / 1900ⁿ-(-4ⁿ) ⇒ 1904/ 1900ⁿ-(-4ⁿ)
⇒ 16/ (1900ⁿ-(-4ⁿ))
Similarly we proceed to show that 125 divides 121ⁿ-25ⁿ +1900ⁿ-(-4ⁿ):
Now, (121-(-4)) / (121ⁿ-(-4ⁿ)) ⇒ 125/ (121ⁿ-(-4ⁿ))
Now, (1900-25) / 1900ⁿ-25ⁿ) ⇒ 1875/ (1900ⁿ-25ⁿ)
⇒ 125/ (1900ⁿ-25ⁿ)
Hence, we have proved that both 16 and 125 divide 121ⁿ-25ⁿ +1900ⁿ-(-4ⁿ) which means that 2000 divides 121ⁿ-25ⁿ +1900ⁿ-(-4ⁿ).