Question

Find the unit digit of the following numeric expression.

114²⁰ + 115²¹ + 116²²

Answer 1

114²⁰ + 115²¹ + 116²²

In 114²⁰ unit digit of base 114 is 4 and power is 20 ...(even power)

∴ Unit digit of 114²⁰ is 6

In 115²¹ unit digit of base 115 is 5 and power is 21 ...(Positive Integer)

∴ Unit digit of 115²¹ is 5

In 116²² unit digit of base 116 is 6 and power is 22 ...(Positive Integer)

∴ Unit digit of 116²² is 6

∴ Unit digit of 114²⁰ + 115²¹ + 116²² can be obtained by adding 6 + 5 + 6 = 17

Unit digit of 114²⁰ + 115²¹ + 116²² is 7