How I solve this problem by python? Please help and give me a idea to solve this.

It is a question from the book **104 number theory problems**.

**Problem**

If x,y,z are natural numbers where x and z are odd numbers and y is a multiple of 8, then how many solutions does the equation given below have?

**x+y+z=2014**

You can solve this mentally.

It’s 126253.

Let’s say it’s

x+z=k//assuming k is even

We have solutions from

1 k-1

3 k-3

5 k-5

…

k-1 1

So the number of solutions is k/2.

Now if y is 8 , we get 2014 - 8 /2 = 1003

if y is 16, we get 2014 - 16 /2 = 999

This goes on until we reach 3

so we get 3+ 7 + 11 … 1003

That sum is 126253.

1 Like

Thanks a lot . I understand your answer and now I can also do it with python easily.

c=0

for y in range(8,2014,8):

p=2014-y

for x in range(1,p,2):

z=p-x

c+=1

print('total number of solutions : ',c)

What is answer given in the book?