Somethings together
Level
pending
- Find 3^100(mod 100). this is 'a'
- Integrate f(3x-1) over 1 to 3. You should get a constant. Let this be 'b'.
- Now let there be a function g(x) which is ax^2+bx.
- What is g(ab)?
- Try not to use wolfram alpha.
The answer is 200.
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The real challenge in this question is finding 3 1 0 0 m o d 1 0 0 .
First of all, we must note that 'mod 100' of any number N means the last 2 digits of N .
Now 3 1 0 = 3 5 ∗ 3 5 = 2 4 3 ∗ 2 4 3
The last 2 digits of 3 1 0 can be found from 4 3 ∗ 4 3 = 1 8 4 9 = 4 9 . So 3 1 0 maybe a b c . . 4 9 .
Similarly last 2 digits of 3 2 0 = 3 1 0 ∗ 3 1 0 = 4 9 ∗ 4 9 = 2 4 0 1 = 0 1
Last 2 digits of 3 4 0 = 0 1 ∗ 0 1 = 0 1
Last 2 digits of 3 6 0 = 3 4 0 ∗ 3 2 0 = 0 1 ∗ 0 1 = 0 1
...
Last 2 digits of 3 1 0 0 = 0 1 = a