What is the remainder when 13 to the 51st power is divided by 5?
131 mod 5 =13 mod 5 = 3
132=169 mod 5 = 4
133=2197 mod 5 = 2
134=28561 mod 5 = 1
135=371293 mod 5 = 3
136=4826809 mod 5 = 4
137=62748517 mod 5 = 2
138=815730721 mod 5 = 1
....
1348 mod 5 = 1
1349 mod 5 = 3
1350 mod 5 = 4
1351 mod 5 = ?
Note:
13^51=647307989872865201422284359961937038113215496061434545237
yolo
To find the remainder when 13 to the 51st power is divided by 5, let's break down the problem step by step.
Step 1: Start with 13 and divide it by 5.
- We get a quotient of 2 and a remainder of 3.
- This means that when we divide 13 by 5, we have 2 groups of 5 with a remainder of 3.
Step 2: Observe the pattern of remainders.
- When we raise 13 to higher powers, the pattern of remainders repeats itself.
- Notice that when we divide 13 to the power of 1 by 5, we get 3 as the remainder.
- When we divide 13 to the power of 2 by 5, we also get 3 as the remainder.
- This pattern continues: for every power of 13, the remainder remains 3.
Step 3: Determine the remainder for the given power.
- Now, we need to find the remainder when 13 to the 51st power is divided by 5.
- Since the pattern repeats every 2 powers, we can rewrite 51 as 50 + 1.
- Notice that the remainder for 13 to the power of 50 is 3.
- Adding 1 more power will not affect the remainder, so the remainder when 13 to the 51st power is divided by 5 is also 3.
Therefore, the remainder when 13 to the 51st power is divided by 5 is 3.