Question

What is the remainder when 3 to the power 256 is divided by 5?

Answer 1

Given : 3²⁵⁶ divided by 5

To find : Remainder

Solution:

3²⁵⁶

= 3⁴ˣ⁶⁴

= (3⁴)⁶⁴

= (81)⁶⁴

Any number ending with 1 having any power ends with 1

=> (81)⁶⁴  ends with 1

Any number ending with 1 when divided by 5

will leave a remainder = 1

=> remainder = 1 when 3²⁵⁶ is divided by 5

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