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The number of ordered pairs (a, b) such that the equations ax + by = 1 and x2 + y2 = 50 have all solutions integral is .....

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x2 + y2 = 50 and ax + by = 1

x2 + y2 = 50 has 12 integral points given by (±1, ±7), (±7, ±1) and (±5, ±5).

If line ax + by = 1 intersects the circle at all integral points, then the number of such lines are 12C1 + 12C2 – 6 = 66.

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