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9 years, 7 months ago
find the remainder when 7^99 is divided by 101
9 years, 7 months ago
Euler of 101 = 100
So, 7^100 mod 101 = 1
7 * 7^99 mod 101 = 1
Let 7^99 mod 101 = k
=> 7k mod 101 = 1
=> 7k = 101p + 1
p = 2 satisfies for k = 29
So, remaninder = 29