Hello all,

I am currently taking a History of Mathematics course at university level.

Unfortunately I am now stuck on one of the questions:

Find a positive integer solution to the equation350x+1 = 99y

Use the technique of Bashkara. Give your answer as the possible smallest integer

I have access to the previous year's solution when the equation was250x+1 = 87y

Euclidean algorithm

250 = 2*87 + 76

87 = 1*76 + 11

76 = 6*11 + 10

11 = 1*10 + 1

Step 2:

2 2 2 2 23

1 1 1 8 8

6 6 7 7

1 1 1

1 1

0

Possible solution:x=8,y=23

I understand step one of the question, and have worked out the following for this year's equation (350x+1 = 99y)350 = 99*3 + 53

99 = 53*1 + 46

53 = 46*1 + 7

46 = 7*6 + 4

7 = 4*1 + 3

4 = 3*1 + 1

3 = 1*3 + 0

But can someone explain to me what is going on in step 2, I am totally lost here.

Thank you very much!