Question

Find the remainder when 3^49+ 9^49is divided by 10?

Answer 1

3⁴⁹ = 3×3⁴⁸ = 3×(3²)²⁴ = 3×9²⁴

10 = 9-1

substitute x for 9 we get

3x²⁴+x⁴⁹ ÷ (x-1)

when f(x) is divided by (x-a) then remainder is f(a)

remainder= f(1) = 3+1 = 4