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A simple number theory problem
Hello everyone!
Today I was solving a problem and I reduced it to finding a maximum of a function. So in short what I need is the following:
, where M, a, b ≤ 109.
It's obvious that 
iff 
, but I cannot find an easy way to get the maximum if 
. I will appreciate any help on the problem.
PS: a, b and M are given as queries so I need an algorithm to answer up to 105 queries.
UPDATE: It's actually pretty simple. 
actually has values of form 
. Then it's obvious that the solution will be 
.
| Rev. | Lang. | By | When | Δ | Comment | |
|---|---|---|---|---|---|---|
| en4 |
|
radoslav11 | 2017-02-07 15:21:06 | 4 | ||
| en3 |
|
radoslav11 | 2017-02-07 15:20:16 | 2 | Tiny change: 'hat $\max f(x) = M - ' -> 'hat $\max g(x) = M - ' | |
| en2 |
|
radoslav11 | 2017-02-07 13:45:12 | 206 | ||
| en1 |
|
radoslav11 | 2017-02-07 12:57:42 | 528 | Initial revision (published) |
