Question

50^th root of x is 12

50^th root of y is 18

Remainder when x + y is divided by 25.

Answer 1

12⁵⁰ + 18⁵⁰ = 144²⁵ + 324²⁵ 

= (25K₁ – 6)²⁵ + (25K₂ – 1)²⁵

= 25λ – 6 25 – 1 

6²⁵ + 1 = (6⁵)⁵ + 1 

= (7776)⁵ + 1 

= (25λ₁ + 1)⁵ + 1

= 25p + 2 

⇒ 12⁵⁰ + 18⁵⁰ = 25λ – (25p + 2) 

⇒ Remainder = 23