Squirrel Chase
You are standing \(250\) metres due North of a Squirrel, at the moment when the squirrel calls out "Catch me if you can!" and starts running due East. Quick on your feet, you immediately start chasing after the squirrel. Instead of running South-East on a straight line, you run so at every instant you are heading directly towards the squirrel. You run \(1.4\) times as fast as the squirrel. Let \(D\) denote the distance that the squirrel ran before you catch it.
| Part A | Find \(D\) in meters, rounded to the nearest meter. | |
|---|---|---|
| Part B | Find \(D\) in millimeters, rounded to the nearest millimeter. |
Integer Factorization
Let \(N = pq\) be a positive integer which is the product of two large prime numbers \(p\) and \(q\). Let \(R\) be the remainder when \(p+q\) is divided by \(10^9+7\). Hint: the difference between \(p\) and \(q\) is less than \(10^{80}\) (the current estimate for the number of atoms in the observable universe).
| Part A | Find \(R\) when \(N = \) 37834082197. | |
|---|---|---|
| Part B | Find \(R\) when \(N = \) 31259182824182977579361. | |
| Part C | Find \(R\) when \(N = \) 279680497756621349605906986937174040586 145180581133159093315713686803955381832 199906939110100292778501757276492336647 733009077451211345797330743124737928346 315459217030828079849109738375831203116 482566885088773675647315143800526347195 967243145966681580005600894548499860991 115107257526176229258827758033769663. |