Q. Find an infinite set of integers x any y such that $\displaystyle 4973x+9743y=h$. 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