and an integer 
you are to write a
program that determines 
, the positive 
root
of p. In this problem, given such integers n and p, p will
always be of the form 
for an integer k (this integer is what
your program must find).
| Problem 113 - Power of Cryptography, Explanations |
Oh, look at this beautiful big integer, prepare your big integer library!
But don't use it!!!
Just cast the big integer into a double, use the math library power function, round it and print it.
This is possible because input never ask to calculate a root small enought so that it stays a big integer.
So the trick : there's no trick!
If you are in trouble with the multi-entry input, read my how to read input.
Current work in cryptography involves (among other things) large prime numbers and computing powers of numbers modulo functions of these primes. Work in this area has resulted in the practical use of results from number theory and other branches of mathematics once considered to be of only theoretical interest.
This problem involves the efficient computation of integer roots of numbers.
Given an integer and an integer you are to write a
program that determines , the positive root
of p. In this problem, given such integers n and p, p will
always be of the form for an integer k (this integer is what
your program must find).
The input consists of a sequence of integer pairs n and p with each
integer on a line by itself. For all such pairs 
,
and there exists an integer k, 
such that 
.
For each integer pair n and p the value should be printed,
i.e., the number k such that .
2 16 3 27 7 4357186184021382204544
4 3 1234