Given two integers A and B where A is not divisible by B, the task is to express A / B as a natural number modulo m where m = 1000000007.
Note: This representation is useful where we need to express Probability of an event, Area of Curves and polygons etc.
Input: A = 2, B = 6
Input: A = 4, B = 5
Approach: We know that, A / B can be written as A * (1 / B) i.e. A * (B ^ -1).
It is known that the modulo(%) operator satisfies the relation:
(a * b) % m = ( (a % m) * (b % m) ) % m
So, we can write:
(b ^ -1) % m = (b ^ m-2) % m (Fermat's little theorem)
Therefore the result will be:
( (A mod m) * ( power(B, m-2) % m) ) % m
Below is the implementation of the above approach:
- Find sum of modulo K of first N natural number
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- Expressing a number as sum of consecutive | Set 2 (Using odd factors)
- Maximum rational number (or fraction) from an array
- Largest proper fraction with sum of numerator and denominator equal to a given number
- Primitive root of a prime number n modulo n
- Find the number of primitive roots modulo prime
- Expressing factorial n as sum of consecutive numbers
- Find all divisors of a natural number | Set 1
- Find if given number is sum of first n natural numbers
- Sum of all proper divisors of a natural number
- Find all divisors of a natural number | Set 2
- Number of compositions of a natural number
- Find the first natural number whose factorial is divisible by x
- Find the k-th smallest divisor of a natural number N
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