Why is it 100 is used to solve the last digit of 49^19 using Chinese Remainder Theorem?
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Hello mate
Your answer
Given:
49^19
To find:
The last two digits.
Solution:
By using Chinese remainder theorem,
x ≡ 49^19 mod 100
100 = 25 * 4
x ≡ 49^19 mod 25
x ≡ 49^19 mod 4
( 49 )^19 = ( -1 )^19 mod 25
-1 mod 25
( 49 )^19 = ( 1 )^19 mod 4
1 mod 4
x ≡ ( ( -1 ) ( 4 ) ( 19 ) ) + ( ( 1 ) ( 25 ) ( 1 ) )
x ≡ -51 mod 100
x ≡ 49 mod 100
Hence, the last two digits of 49^19 is 49.
Hope it helps.
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giankarlocatapang09:
Hello mate,
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