If 5^{99} is divided by 13, then the remainder is ?

Brenton Marks

Brenton Marks

Answered question

2023-02-06

If 599 is divided by 13, then the remainder is ?

Answer & Explanation

Scarlet Barrett

Scarlet Barrett

Beginner2023-02-07Added 6 answers

Given
5 99 = 5 ( 5 ) 98 = 5 ( 25 ) 49
= 5 ( 26 1 ) 49
= 5 [ 49 C 0 ( 26 ) 49 49 C 1 ( 26 ) 48 + 49 C 2 ( 26 ) 47 + 1 ]
= 5 [ 26 k 1 ] , k Z
Then,
5 99 13 = 5 [ 26 k 1 ] 13
= 10 k 5 13 = 10 k 1 + 8 13
Thus, the remainder is 8.

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