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Calculate the modulo operations given below: 7⁵ mod 15 =

User Byzantian
by
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2 Answers

4 votes

Answer: 7

Work Shown

7^2 = 49

Divide this over 15 and we get 49/15 = 3 remainder 4

This would mean
7^2 \equiv 4 \ (\text{mod 15})

The modulo cares only about the remainder.

Square both sides.


7^2 \equiv 4 \ (\text{mod 15})\\\\(7^2)^2 \equiv 4^2 \ (\text{mod 15})\\\\7^4 \equiv 16 \ (\text{mod 15})\\\\7^4 \equiv 1 \ (\text{mod 15})\\\\

The last step is to multiply both sides by 7.


7^4 \equiv 1 \ (\text{mod 15})\\\\7*7^4 \equiv 7*1 \ (\text{mod 15})\\\\7^5 \equiv 7 \ (\text{mod 15})\\\\

Therefore, the calculation (7^5)/15 results in some quotient and a remainder of 7.

User Javier Cuervas
by
7.1k points
7 votes

Answer:

7

Explanation:

To calculate 7⁵ mod 15, we need to find the remainder when 7⁵ is divided by 15.

Let's break down the steps to simplify the calculation:

Step 1: Calculate 7⁵

7⁵ = 7 × 7 × 7 × 7 × 7 = 16807

Step 2: Divide 16807 by 15

16807 ÷ 15 = 1120 remainder 7

Step 3: The remainder is the result of the modulo operation

So, 7⁵ mod 15 = 7

Therefore, when we calculate 7⁵ mod 15, the answer is 7.

User Maztch
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8.1k points