5^20+5^7/7=? Reminder is…………
5^20+5^7/7=? Reminder is…………
Answer/Solution
2
Steps/Work
5^20 mod 7 + 5^7 mod 7
Since 5 nd 7 are co-primes, we can use Euler's theorem
E(7) = 6
So 5^E(7) = 1
5^20 mod 7 => (5^6)^3 * 5^2 mod 7
1 * 25 mod 7 = 4
Similarly 5^7 mod 7 => 5^6 * 5 mod 7
1 * 5 mod 7 = 5
Now 4 + 5 mod 7
9 mod 7 = 2
ANSWER:B
Since 5 nd 7 are co-primes, we can use Euler's theorem
E(7) = 6
So 5^E(7) = 1
5^20 mod 7 => (5^6)^3 * 5^2 mod 7
1 * 25 mod 7 = 4
Similarly 5^7 mod 7 => 5^6 * 5 mod 7
1 * 5 mod 7 = 5
Now 4 + 5 mod 7
9 mod 7 = 2
ANSWER:B