# Find First element in AP which is multiple of given Prime in Python

Suppose we have a first term (A) and common difference (d) of an AP series, and we also have a prime number P, we have to find the position of the first element in the given AP which is the a multiple of the given prime number P.

So, if the input is like A = 3, D = 4, P = 5, then the output will be 3 as fourth term of the given AP is a multiple of the prime number 5. So, first term = 3, second term = 3+4 = 7, third term = 3+2*4 = 11 and fourth term = 3+3*4 = 15.

To solve this, we will follow these steps −

• Define a function get_pow() . This will take x, y, p

• ans := 1

• x := x mod p

• while y > 0, do

• if y AND 1 is non-zero, then

• ans :=(ans * x) mod p

• y := y/2

• x :=(x * x) mod p

• return ans

• From the main method, do the following −

• A := A mod P

• D := D mod P

• if A is same as 0, then

• return 0

• otherwise when D is same as 0, then

• return -1

• otherwise,

• X := get_pow(D, P - 2, P)

• return(X *(P - A)) mod P

## Example

Let us see the following implementation to get better understanding −

Live Demo

def get_pow(x, y, p) :
ans = 1
x = x % p
while y > 0 :
if y & 1 :
ans = (ans * x) % p
y = y >> 1
x = (x * x) % p
return ans
def get_nearest(A, D, P) :
A %= P
D %= P
if A == 0 :
return 0
elif D == 0 :
return -1
else :
X = get_pow(D, P - 2, P)
return (X * (P - A)) % P

A = 3
D = 4
P = 5
print(get_nearest(A, D, P))

## Input

A = 3 D = 4 P = 5

## Output

3