I don't why there is Run Time ERROR (for higher values of a,b,c) even in time complexicity O(n).

for _ in range(int(input())):
    a,b,c=map(int,input().split())
    x=int(c/(a+(b/a)*b))
    m,n=x,x
    while True:
        if m>0:
            y=(c-a*m)/b
            if y==int(y):
                print(str(m)+" "+str(int(y)))
                break
            m-=1
        y=(c-a*n)/b
        if n>0 and y==int(y):
            print(str(n)+" "+str(int(y)))
            break
        n+=1

This is not a geometry exercise

Hi,

There seems to be something wrong with this problem :

The linear diophantine equation a*x+b*y=c hasn't always integer solutions, if no constraint at all is imposed to a, b, and c.

The following wikipedia article (in french) explains it :

linear diophantine equation (french)

Sorry, but the article on Wikipedia is only available in French.

Best regards

can anybody give some hints?

I think there is another error in the testcases.

Testcase 2

• Item #12
• Input: 4 1 82
• Testcase Solution: 19 6 (4*19+6 = 82)
• Correct Solution: 1 78 (4*1+78 = 82)

Testcase 3

• Item #73
• Input: 30 3 69
• Testcase Solution: 2 3 (2*30 + 3*3 = 69)
• Correct Solution: 1 13 (1*30 + 13*3 = 69)