Question

Computing exponents mod m. Compute each quantity below using the methods outlined in this section. Show your steps, and remember that you should not use a calculator. (a) 4610 mod 7 (b) 345 mod 9 Calculation of integers based on div and mod. (a) n div 5 = -10, n mod 5 = 4 (b) n div 11 = -3, n mod 11 = 7 (c) n div 10 = 2, n mod 10 = 8

Name: computing exponents mod m compute each quantity below using the methods outlined in this section show your steps and remember that you should not use a calculator a 4610 mod 7 b 345 mod 9 ca 06058
Uploaded: 2023-10-26T00:06:56-08:00
Duration: 4 min 46 s
Channel: Supreeta N
Description: computing exponents mod m compute each quantity below using the methods outlined in this section show your steps and remember that you should not use a calculator a 4610 mod 7 b 345 mod 9 ca 06058

          Computing exponents mod m.
Compute each quantity below using the methods outlined in this
section. Show your steps, and remember that you should not use a
calculator.
(a)   4610 mod 7
(b)    345 mod 9
Calculation of integers based on div and mod.
(a)   n div 5 = -10, n mod 5 = 4
(b)    n div 11 = -3, n mod 11 = 7
(c)   n div 10 = 2, n mod 10 = 8

Added by Briana B.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Supreeta N

10/26/2023

Step 1

This is known as Fermat's Little Theorem. Since $7$ is prime and $46$ is not divisible by $7$, we have $46^{6} \equiv 1 \pmod{7}$. Now, we can write $46^{10} = (46^{6})^{1} \cdot 46^{4}$. Using the property, we get: $46^{10} \equiv 1^{1} \cdot 46^{4} Show more…

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Computing exponents mod m. Compute each quantity below using the methods outlined in this section. Show your steps, and remember that you should not use a calculator. (a) 4610 mod 7 (b) 345 mod 9 Calculation of integers based on div and mod. (a) n div 5 = -10, n mod 5 = 4 (b) n div 11 = -3, n mod 11 = 7 (c) n div 10 = 2, n mod 10 = 8