Question

The value of 3⁵¹ mod 5 is _________.

Answer 1

Calculation

3 mod 5 = 3

9 mod 5 = 4

27 mod 5 = 2

81 mod 5 = 1

243 mod 5 = 3

729 mod 5 = 4

2187 mod 5 = 2

6561 mod 5 = 1 and so on

Repeating sequene: {3, 4, 2, 1,}

3⁵¹ mod 5 = (3^{4 × 12 + 3}) mod 5 ≅ 3³ mod 5 = 2

Therefore, the value of 3⁵¹ mod 5 is 2.

Tips and Tricks:

For this expression, aspirant can get the answer directly from the GATE calculator, but it is not always the case. Hence go through the standard procedure each time this question is asked.