# Thread: Finding infinite set of solutions, X and Y

1. ## Finding infinite set of solutions, X and Y

Q. Find an infinite set of integers x any y such that $4973x+9743y=h$. Write answer in terms of the arbitrary integer L (Lambda, hehe).

Here's what I've got:

(i) First find HCF

(after euclidean algorithm) = 1.

(ii) Find x and y integers
1=203-202
1=203-(4770-4669)
1=(24)203-4770
1=24(4973-4770)-4770
1=24(4973)-25(4770)
1=24(4973)-25(9743-4973)
1=24(4973)-25(9743+25(4973))
1=40(4973)+9743(-25)

So x = 29 and y = -25 (it is already wrong, LHS does not = RHS)

But I persisted

(iii) X = 49 + 9743L (lambda), Y=-25-4973L
eg let L = 100

Oh dear it's wrong :C

Any help on this? I think I stuffed up during the arithmetic, as usual

2. Hello RAz
Originally Posted by RAz
1=203-202
1=203-(4770-4669)
You went wrong on line 2! Here's what I got:

1 = 203 - 2 . 101

= 203 - 2 . (4770 - 23 . 203)

= 47 . 203 - 2 . 4770

= 47 . (4973 - 4770) - 2 . 4770

= 47 . 4973 - 49 . 4770

= 47 . 4973 - 49 . (9743 - 4973)

= 96 . 4973 - 49 . 9743

So $x = 96 + 9743\lambda$ and $y = -49 - 4973\lambda$