173x+197y=149,197x+173y=221
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1990 = 173 x 11 + 87
173 = 87 + 86
87 = 86 + 1
thus 1 = 87 - 86 = 87 - (173 - 87) = 87(2) + 173(-1) = (1990 - 173 x 11)(2) + 173(-1)
ie 1 = 1990(2) - 173(23)
multiply by 11, we have 11 = 1990(22) - 173(253)
therefore (22, 253) is an integral solution of 1990x - 173y = 11
let x = 22 + 173t and y = 253 + 1990t
we have 1990(22 + 173t) - 173(253 + 1990t) = 1990(22) - 173(253) = 11
thus (22 + 173t, 253 + 1990t) are integer solutions for all integer value of t
173 = 87 + 86
87 = 86 + 1
thus 1 = 87 - 86 = 87 - (173 - 87) = 87(2) + 173(-1) = (1990 - 173 x 11)(2) + 173(-1)
ie 1 = 1990(2) - 173(23)
multiply by 11, we have 11 = 1990(22) - 173(253)
therefore (22, 253) is an integral solution of 1990x - 173y = 11
let x = 22 + 173t and y = 253 + 1990t
we have 1990(22 + 173t) - 173(253 + 1990t) = 1990(22) - 173(253) = 11
thus (22 + 173t, 253 + 1990t) are integer solutions for all integer value of t
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