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a_{2n}-ba_n is square, if a_n is positive integer with n digits all =1, b digit

Source: Vietnamese MO (VMO) 1974

August 20, 2018
number theoryDigitspositive integer

Problem Statement

Find all positive integers nn and bb with 0<b<100 < b < 10 such that if ana_n is the positive integer with nn digits, all of them 11, then a2n−bana_{2n} - b a_n is a square.
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