Prove that in each set of ten consecutive integers there is one which is coprime with each of the other integers.

For example, taking 114, 115, 116, 117, 118, 119, 120, 121, 122, 123 the numbers 119 and 121 are each coprime with all the others. [Two integers a, b are coprime if their greatest common divisor is one.]

[IrMO 2000 Paper 2 Question 4]

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