Observe that 1| (77 7), 2| (77 7), 3| (7777 7), 4| (777...

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Observe that 1| (77 – 7), 2| (77 – 7), 3| (7777 – 7), 4| (777 – 77), 5| (77 7), 6 | (7777 – 7), 7| (77 – 7), 8| (7777 – 777), and 9| (7777777777 – 7). Prove that for every positive integer n, there exist i and j with 1<i<j<n+ 1 such that n is a divisor of 77...7-77...7. jdigits i digits Observe that 1| (77 – 7), 2| (77 – 7), 3| (7777 – 7), 4| (777 – 77), 5| (77 7), 6 | (7777 – 7), 7| (77 – 7), 8| (7777 – 777), and 9| (7777777777 – 7). Prove that for every positive integer n, there exist i and j with 1<i<j<n+ 1 such that n is a divisor of 77...7-77...7. jdigits i digits