Friday, May 9, 2014

A test for divisibility by 17

Again, separate the candidate number into groups of two digits starting from the end. For example, 1178508 = 1 17 85 08. Starting from the beginning of the number, eliminate each group of two digits only this time by subtracting it from the next. Continuing the example, 17-2 =15, 15 85 08, 85-30=55, 5508, 8-110 = -102 + 170 = 68 = 4*17 = 0 modulo 17. Simplify at each stage of the process for unwieldy results.

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