Question

what is the remainder when 3 raised to 50 + 1 is divided by 10​

Answer 1

Answer:

According to the question, In 3^50 +1, as 9+1=10, the unit digit will be always 0

Answer 2

Answer: 0

Step-by-step explanation:

This problem can be easily solved using congruences in elementary Number Theory , but I will explain it to you in the simplest manner .

By manual checking  , you can easily observe that $3^4$ leaves a remainder 1 when divided by 10 (3^4 = 81 , 81/10 gives 1 as remainder)

Now note that $3^8$ also leaves a remainder 1 when divided by 10 . (Since 3^4 is 81 , 3^8 is 81 x 81 , since both give a remainder of 1 , we eventually have the remainder 1x1 = 1 when divided by 10)

Similarly by using this pattern in the end we get 3^48 leaves a remainder 1 when divided by 10 (using the same logic)

We know that 3^2 or 9 gives 9 a remainder when divided by 10 .

Therefore, 3^50 = 3^48 x 3^2 = 1 x 9 = gives 9 remainder when divided by 10 .

So we have 3^50 + 1 , 3^50 gives 9 remainder , 9 + 1 = 10 , which is actually divisible by 10 .

Therefore 3^50 + 1 gives 0 as remainder when divided by 10 .

(You can check this in the calculator as well using the mod function)