Find 5 1024 3130 mod 13Solution5 1024 3130 mod 13 First

Find (5 ¹⁰²⁴ + 3¹³⁰ ) mod 13.

(5 ¹⁰²⁴ + 3¹³⁰ ) mod 13

First we look at powers of 5 mod 13

5=5 mod 13

5^2=25=-1 mod 13

5^4=(5^2)^2=(-1)^2=1 mod 13

So, 5^{1024}=(5^4)^{256}=1 mod 13

Now we look at powers of 3 mod 13

3^3=27=26+1=1 mod 13

3^{130}=3^{129+1}=3*3^{129}=3*(3^3)^{43}=3*1 =3 mod 13

So,

(5 ¹⁰²⁴ + 3¹³⁰ ) =1+3 mod 13=4 mod 13

$Find (5 1024 + 3130 ) mod 13.Solution(5 1024 + 3130 ) mod 13 First we look at powers of 5 mod 13 5=5 mod 13 5^2=25=-1 mod 13 5^4=(5^2)^2=(-1)^2=1 mod 13 So, 5^{$

Find 5 1024 3130 mod 13Solution5 1024 3130 mod 13 First

Solution

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