Finding the last two digit
Find the last two digits of
2 5 5 5 7 5 9 8 3 2 .
The answer is 81.
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2 solutions
What inspired you to realize that 5 9 5 ≡ − 1 ( m o d 1 0 0 ) ?
How about a number which is 2^12424536436234635415262456 ?
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The last digit is 2.
Since 1 2 4 2 4 5 3 6 4 3 6 2 3 4 6 3 5 4 1 5 2 6 2 4 5 6 ≡ 0 ( m o d 4 ) , so it is 6.
The last digit of 2 5 5 5 7 5 9 8 3 2 is equal to 9 2 , so 1 .
The second digit is 8 . So, 8 1 .
2 5 5 5 7 5 9 8 3 2 ≡ 5 9 8 3 2 ≡ ( 5 9 5 ) 1 6 6 ⋅ 5 9 2 ≡ − 1 1 6 6 ⋅ 8 1 ≡ 8 1 ( mod 100 )