What is the remainder of 3^29 divided by 4?

2 Answers
Feb 25, 2018

Since 29 is an odd number,
the remainder happens to be 3

Explanation:

3^29/4
when 3^0 =1 is divided by 4, the remainder is 1
when 3^1 =3 is divided by 4, the remainder is 3
when 3^2 =9 is divided by 4, the remainder is 1
when 3^3 =27 is divided by 4, the remainder is 3
ie
all the even powers of 3 has remainder 1
all the odd powers of 3 has remainder 3

Since 29 is an odd number,
the remainder happens to be 3

Feb 25, 2018

3

Explanation:

If you look at the pattern of 3^x/4 you see the following:

3^1/4=.75

3^2/4=2.25

3^3/4=6.75

3^4/4=20.25

3^5/4=60.75

3^6/4=182.25

etc.

You could make a conjecture that if the power is even, then the decimal part of the answer is equivalent to 1/4 or stated differently, the remainder is 1. If the power is odd, then the decimal part of the answer is equivalent to 3/4 or stated differently, the remainder is 3. Therefore, 3^29/4=(SomeGiantNumber).75, so the remainder is 3.